I am not sure what other ways there would be to actually perform this in order to profit, but wouldn't doing arb with existing balances on exchanges work in a similar fashion than waiting for the funds to be deposited?
If you do not want to risk losing the price when doing Arbitrage, better do not do it. Because I also did it and did not make a profit because of the long delivery time that made me angry. But I should be grateful, because the benefits I get more than the losses that I received.