Roman,
Not to worry.
I added 6-12" wavy additions to a concrete patio 20 years ago in preparation for flagstone overlay. Flag, though thicker, will not handle any movement without debonding or, more often, cracking the stone. I had zero issues over 20 years and considering the new add-on material was only supported on one side, that is a sign, through Arizona snow and 120 degree heat that the process was a good one. Your garage floor in Oregon will likely never see those extremes.
I would cut whatever you want with the following provisos.
The wider cuts can be drilled and re-barred every 12 inches with 3/8 or 1/2" rebar. You don't even need to epoxy them if the hole drilled in the existing concrete is 4" deep, or more. The rebar will hold on just fine. See A below...
The problem with your narrow control line cut is, you cannot drill in a narrow gap very easily. An alternative I have used successfully is B below. Bevel the cut slightly and then dig under the existing slab a couple inches along the trench. The new poured cement will lock itself into position and cannot sag or heave. I did this under my shower floor where I had to move my drain 6" after a total re-model of the shower. The tile on the floor is natural polished stone rocks about 1-2 inches across. Even with hot water in winter there is zero movement on that slab repair.
Cutting at a slight bevel is easier said than done! It doesn't take much to lock the old and new slabs together. Depending on your concrete saw, you can eitheryob a few feey of tape around one of the saw wheels or, get some 1/2" plywood or other material and put it under one of the wheels to keep your saw at an angle. Concrete cutting is kinda fun. The saws run $85 for four hours at Homey 'Po and they charge for a blade. Take my advice and just buy a good blade for $100 and use it for other cuts when you rent the saw again.
Pardon my Crayola drawings...
As for the repair cracks, and your shrinkage cracks, or small cracks from settling that nearly every floor ever poured has, I just used RedGard as an isolation membrane. The fabric membrane I mentioned in my article was both expensive and made by another manufacturer. Custom guarantees your floor from cracking when using their products. So, I just went with the crack isolation mortar and RedGard spread a couple feet either side of the major cracks. Worked great!
In my house garage, I am doing the same thing, only going with FlexBond White Crack Prevention Mortar instead of the heinously expensive stuff I used in the shop. I am also going to use a 3/8 trowel instead of 1/2" to thin out the base just a tad. I laid the office 20" tile with that and it worked out much easier keeping the tiles flat. Thick mortar allows the tile to get a little "tippy." Its the thicker mortar that helps with crack isolation but, taking 1/8" out won't hurt anything and I'll get more consistent lays.
Some people think saw-cutting your slab is insanity. My wife was unsure until she watched me cut the slab in our living room to add a floor plug. Using the water spray to cut dust to zero, you make a little mud. No biggee. Once you get the cut complete, you pull the pieces out and hose the mud back into the trenches. You end up very clean afterwards. Just wear headphones. Its loud. I think I cut over 100' of slab and patio in seven or eight areas during this remodel. No problems with any of them. Glad I bought a blade three-pack! Oh... and one last thing: Termites. Not that you'll get termites eating up your concrete but, I always like to leave the buggers something should they get under my slab. The night before pouring the concrete repair, I always pour a bucket of Termidor into the area and let it soak in. That takes care of termites for a decade. See these guys for great prices...
http://www.domyownpestcontrol.com/termidor-sc-p-184.html
Hope that helps.
Ray
