I'm *not* a vet pvp battler, but I have been thinking about your question and want to make a suggestion towards something almost like an answer.
It seems to me that your current team would do well because it is based around three pets that are very strong on their own, not because of synergy or some specific tactic needed for success every time, and also because you have a decent variety of attack types. As such, if you want to change things around a bit, maybe just try rotating in other different strong pets. For example, drop your moth for a different bird, such as a junglebeak, which shouldn't be too strange for you at first to adjust to (still a hard-hitting flier) but which has different abilities to play around with.
Alternatively, split them up and make 3 different teams, each one with one of the pets that you are familiar with. Make a bleeding-synergy team with your rabbit, or a clonedance team with your blighthawk, and see how that goes.
Really, since this game doesn't track losses, there's no need to be scared of experimenting.
In case, of course, you really really really don't like losing, in which case, ignore what I said!