Okay I did a full test for you.
I used a Classic Systainer 3.
-> Used the screw-boxes tray bottom (this:
http://www.systainerworld.com/Tanos_Tray_p/447-337.htm)
-> Put in the screw boxes.
-> I did not have one of the hard foams on hand. But I'm familar with them, as I have two of the screw boxes. Instead, I put the Systainer base foam over the boxes. This:
http://www.systainerworld.com/Tanos_Base_foam_for_Systainer_I_V_p/446-573.htm
-> Put in a pair of Mini-Sys. -> Also tried it with a pair of Mini-Sys IIs
Results:
>> You will have to do some slight cutting to the tray, as Seth noted, beause the Sys 3 taper at the bottom much more than a Sys1.
>> I would recommend you have a look at using the base foam noted above.
This foam is about 3/8" thick, and is not a pick-n-pluck. I think it'll work better than the hard foam, because the hard foam is shaped for the recesses of the Systainer lids (unless you want to spend some time with a Xacto knife).
>> If you use regular Mini-Systainers, then a lid foam (with the egg-crate bumps) will be necessary. There is about 1/2"+ space above the Mini-Sys.
>> If you use Mini-Sys IIs, you probably won't need the lid foam. They get much closer to the lid. There will not be pressure, per se, on the foam and screws. But there won't be a lot of play, either. Don't know if you're familiar with the Mini-Sys IIs, but they're 3/4" taller which translates to a lot more utility (IMO).
Cheers