This is long; sorry, but to be meaningful it needs to be.
All joking aside, here’s an attempt at some constructive suggestions. I am an engineer and designer for a living, so deal a lot with trying to fit peoples dreams, wants and desires into reality in the space they are having designed. I’ll try to address your space specifically.
The design of the garage is a typical, residential 3 car garage such as is found on most upper level suburban subdivision homes. Great for resale, not necessarily for shop use. What you described as your wants are shop use. Plus suburban storage. Plus vehicle garage. You describe storage needs of a 72” SO roller, a oversize sink, 4 bikes hung up, 2 strollers hung up, a large air compressor in an enclosed area, a lift, attic storage space, and talk about having a family. A typical family uses most of this garage space for storage; occasionally they are able to fit 1 or 2 cars into it. At least part time.
You also have talked about making do in the past, by parking your vehicles outside so you could rebuild a transmission and working around the space you have. You talk about dealing with what you have in the future. If that’s the approach you want to take, just forge ahead with your plans. Or, look at how you can make changes to both your space, and your wants/needs/desires, and come up with a better overall situation. I always look at ways I can change things administratively or procedurally before I make the investment in space and resources to build something.
Here's where I’d go with procedure:
Do you need to store 3 vehicles in the garage? Since one is a project, do you really need 3 active doors?
Do you need to store 4 bicycles and 3 strollers in the garage?
Do you really have a need for a large air compressor? And the closet for it?
Do you really need a lift, and willing to budget the space for it? Have you realistically analyzed what space the lift takes?
What are your realistic storage needs? Can they be met with an inaccessible attic? What will your increasing family do to the storage needs? What kids toys, bikes, strollers, wagons, dirt bikes, 4 wheelers, skate ramps, etc will you need to store and have access to use?
Do you really want/need a project car, and can you give realistic time to completing it? Is it your critical spare time activity, so you are willing to devote the real space you need for it?
The answers to those procedural questions give the final design criteria.
Here’s where I’d critique your design.
The minimum width for 3 workable vehicle bays is: 2 feet from wall to door, 8 foot door, 2 feet space, 18 foot door, 2 feet from door to wall. That’s 32 feet. Minimum. You can cram in 2 feet tighter, if you accept that you can minimally move around the vehicles, it will be hard to get in and out the doors. This will give you no storage of any usable kind on the side walls. The land cruiser is about a 17 foot long vehicle. Give 2 feet clear to the garage door, and 3 feet to minimally move in front of the vehicle and you’ve got 22 feet depth. So, minimum garage parking size is 32 x 22 feet. Working and storage space needs to be added to that. You’re 6” too narrow, but can cramp up to live with that. You’ve got 4 feet of depth left to meet your working and storage needs.
4 bikes and 2 strollers hung in an 8’ ceiling: need 4’ depth, x 24” width to hang and access them: You’ve used up 12 feet of width, 3 feet deep. 6 foot rolling cabinet. Air Compressor 3 feet minimum. 4 foot sink. You’ve used up 28 feet of the 31’6” you plan. You have 3’6” for your slat wall storage and other storage stuff.
So, you’ve managed to cram in the minimum of stuff that you want, and have no space left over for lift, work space, work benches, family storage of stuff, garage and house supplies storage, garbage and recycling, ladder, yard tools, lawn mower, etc.
So, how can you go about increasing the pie? Add an attic? Good plan. Make sure you have access space for a ladder. If you use pull down, you’re making the space less usable, so only low use stuff will be up there. Plus, the pull down has to be in a clear spot on the floor, or you’ll have to move a vehicle to use it. The garage doors block access to a lot of the ceiling. Plan on putting the stairs over the 3 foot aisle between the vehicles and the 4 foot of storage against the back wall.
You can also increase the pie easily by eliminating half the mud room. That room is what we call a “bowling alley” in the house sale world. A bowling alley room in a house DECREASES the value. It isn’t usable. Chart out what is door swing and corridor space, and you’ll see there’s only room for a set of shelves. Split the space in half, and you move that corridor space into the garage, it’s still in the same space, but you’ve added usable shelf and working space to the garage, in excess of what you took out of the house. You’ve also made it much easier to move around and access the garage space. Essentially you shared corridor space so increased the usable area.
You can add a permanent stair to the attic storage. That will allow you to reliably use that space, and you’ve given your family a needed storage area. You can make that stair steep (ship ladder) if you keep your size down below the code minimum for an alternative stair design. That way you minimize the impact on the usable garage space. You’re trading a small amount of garage space for a larger amount of attic storage.
You still haven’t accommodated your lift. The garage doors and your walking corridors and your ceiling height and desire for attic storage use up almost all the floor room. A lift can’t work without compromise, at all. You can install a lift, and park under it, walk over it, and have it in the way. It’ll gut the usability of the garage for workspace and car storage. It’ll need a higher ceiling, and reduce the available attic area for your storage. To get a lift in effectively, you need to go bigger. Here’s where I’d really start to ask if a lift is needed. It’s an expensive, space hogging luxury. Unless you do work that really needs it, and is valuable enough to either hog the space or make you buy more space, I’d abandon that idea. Buy some good jack stands and a decent floor jack.
Back to air compressor. Air compressors are space hogs and noisy. What do you do that needs air? Can you use battery or cordless tools instead? Many guys are going that way. Can you get a small pancake compressor and store it between uses? That’s a compromise a huge number of suburban garages make.
Can you put a garden shed in to store your yard tools and lawn mower and similar stuff? Can you put a garbage can area outside so the garbage isn’t inside?
Here’s where I’d go with my recommendation.
Decide you’re going to have a 2 car vehicle storage garage, with the third bay a work and storage area. Use the wall where the door was for slat wall storage or workbench or shelving. Eliminating one door gives you ceiling room, wall space, and lets you use all the area, not use part of it for door access. Put in one large door for 2 car access and leave one side of the garage for workspace. You don’t need a door for a project car space, just use wheel rollers to move it sideways from the other bays. Add a staircase up to the attic storage, and maximize that attic storage to keep junk out of the garage working space. A usable stair is the prerequisite for that. A ladder or pull down won’t get used much. Add 8 feet of depth to the garage, to provide storage space for the bikes, strollers, tools, sink, workbench, etc. Go to a small portable air compressor, or install in the attic or doghouse outside to save valuable garage space. Eliminate the bowling alley mud room, and block it out into a smaller, more usable space. Use the remainder of the space to provide workbench or cabinetry or storage, and a corridor inside the garage to the back door; you’ll have the same functionality and more usable space. Eliminate the lift. If you can’t do that, you’ll need to increase ceiling height, use scissor or vault trusses to make lift height, and eliminate most, if not all, of the attic storage space. Or, make the garage a lot bigger. It’s a hard trade off to make, and only you can judge what is most valuable to you.
. You might want to vault it for a couple of trusses to put in a lift and put in some attic storage. Put in a good solid stair to the storage, it's worth it to be able to store stuff like engines and spare parts and welders and stuff up there. There's a lot of designs on here of guys that have vaulted a couple of their trusses to put in a lift; it saves money if you just put in the trusses and then loft it later for the lift after the inspection is finished. Putting in a lift would be bad ***; put aside a bit of your overtime each week and you'll have it paid for in no time; when you get it in, then you can loft the trusses. 
