The base unit in these packs is a cell that is 135mm tall, 100mm wide and about 4mm thick. This is a 5Ah cell. The 10Ah packs have 24 of these cells wired as a 12S, 2P pack, making each 10Ah sub pack about 135mm x 100mm x 8mm. you also need to allow space for the BMS circuit board, which for a 12 unit pack is smaller than the footprint of one cell, but around 12 to 15mm deep.
Looking at the space you have available, I think you should be OK. You would need a pack that's made up of three stacks of 8 cells, laid side by side, with the BMS stuck on top. The basic stack of cells would measure about 300 x 135 x 40, with the BMS bringing the thickness up to about 55mm.
Jeremy
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