Thus far, the site has actually lost me a bit of money, just from random variance in bet winnings.

Maybe it's not due to random variance, because there is one thing that is not random: the per-play limit is dynamic and algorithmic. As such, it may be exploitable.

Any time the house has a big loss, the per-play limit is immediately reduced. So there's not so much chance for the house to have a big win on the next bet. In the long run, maybe the house's "big losses" are bigger than its "big wins".

I'm not sure how this interacts with players' typical betting strategies. But it's definitely worth increasing your working capital to the point where you can offer a stable maximum stake, before you decide that your losses are due to random variance.