Since Santa brought me a TR04 Pro here is the answer to the problem:
I have an old Corally 4200 with a quite low rectangular case, it fits. Unfortunately my 5600 LRP's don't because of the "Sub C bulges".
A new Gens Ace 5000 pack would probably fit but mine has become a bit bulgy and therefore would get in contact with the main drive shaft.
So eventually I found a good use for my Carson round case packs which I originally bought for Tamiya Euro Cup races 
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My fleet:
Team C TR04 Pro,Kyosho Lazer ZX, Kyosho Optima, Kyosho Optima MID, Kyosho Optima MID Custom, Tamiya Manta Ray, Kyosho Ultima, Ultima Pro and Ultima Pro II, 3 Kyosho Scorpions, Kyosho Beetle, Kyosho Tomahawk, Kyosho Gallop MK2, 2 Tamiya Grasshopper I, Tamiya Buggy Champ, Tamiya Hornet, Tamiya Frog, Tamiya Wild One, Tamiya Fast Attack Vehicle, Ansmann Mad Rat, Tamiya TB-03, 2 Tamiya TT-01, Tamiya TT01R, 2 Tamiya XC's, RC4WD Gelande Landrover, Axial SCX10
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