7750s are not bad cards at all, but I'm not sure if getting 3 of those would be best.
I dont think there is any other way to get more compute is the chassis. I can modify the 2x8 left riser to accept x16 cards, but they have to be single slot, preferably low profile as well. That way I can offset them so they wont starve each other for air. The right riser is half height only (also x8, modifiable to accept x16).
Even with the cost of the cards added in the whole system will have less than 500 invested.
Cant fit a dual slot card in either as their heat output is hard to control when the fan shroud actually touches the case.