How would a batfish do with these fish?

I would think compatibility would be fine...although I've seen several monos get aggressive with each other and I don't know how an aggressive mono would treat a bat. The only thing I'd be worried about is the height of your tank. If you manage to keep this beauty to maturity (I've been told their survival rate is not so good), I don't know that your tank will be tall enough for it.

Hi GoldFish: There are several types of "batfish". Platax orbicularis. This is more of a round type fish. Platax teira is a tall fish, Taller than it is long. The last is a Platax pinnatus. This is the most famous since it's colors are a striking Black and orange. The orbicularis and teira can get quite large, but it looks like your tank should handle it. My teira was 12" tall but only 5" from nose to tail. They are first inline for feeding but can lost out to smaller faster fish. Also they have some trouble with other fish nipping at their fins. Mine was a great community fish and did quite well. The pinnatus can be more delicate that the others I would only recommend them to experienced fish keepers. HTH's

I wouldn't mix a puffer with any batfish - that's just too tempting of a target for the puffer. Monos might work, but batfish do best in low-key environments with other passive, slower fish.