To the OP: You said you wanted thick foam liners. I don't know how thick you mean, but those three drawers are thin. I used 1/16" sheet cork for liners in mine, and they almost prevent a couple of my larger screwdrivers from clearing the drawer above. Stuff isn't going to move around in the box once it's full, so IMO, the thinner the liner, the better.
And yes, depending on what you're working on, you might get away with 3/8" drive only. I couldn't, and really wouldn't want to regardless, but that was just me.
As far as tool organizers go, I doubt many people have been able to pack more in one of those than I have in mine, and that's with only socket rails or trays, and one tool roll for organizers. You have to pile and jam stuff in those boxes to have enough tools, especially in the top till, which is the only place larger or longer tools will fit.
Here's mine just for comparison. Many of you would probably choose a number of different things, but this is what worked for me based on what I had to work on, mainly 40s-50s vintage American cars and trucks at shows or swap meets.
Cantilever tray has full set of 1/2" regular and deep sockets, plus a few odds and ends.
Till has small and medium ball-peen hammers, medium soft-faced mallet, chisel and punch roll, 2 pair Vise-Grips, all the 1/2" drive tools, adjustable wrenches from 4" to 12", 1/2" and 3/8" speed wrenches (no power at swap meets back in the day, and battery tools were still in the future), combo wrenches from 13/16" to 1-1/4" and a set of 3/8" deep sockets.
What appears to be more space in front is where the cantilever tray drops down, so zkling's suggestion for removing the tray might help, but it also serves as a built-in organizer, so I'd personally not want to remove it.
Top drawer has 1/4" and 3/8" drive and all the accessories, plus set of nut drivers, long hex wrench set and folding hex wrench. At one time, I also had 1/4" and 3/8" drive metric sockets in there just in case. Don't ask me how I managed to get the drawer closed.
Most of you would probably do away with the nut drivers, since you can do almost the same with 1/4" drive sockets and adapters, but they came in very handy for me.
Middle drawer has screwdrivers and various open-end, box-end and combo wrenches up to 3/4".
Bottom drawer had an assortment of pliers and metric combo wrenches. No photo because it's no longer the way it was when I used the box as a road/rally box.
Cantilever box I carried along to have enough tools had a hack saw, pipe wrench, couple of pry bars, small assortment of gear pullers, miniature timing light small VOM and compact tach-dwell-RPM meter, none of which would have fit in the Craftsman box without taking up way too much valuable space.