I don't know how effective these methods are, but I am going to be doing the following in an attempt to not burn myself out also!

1) Not doing friendly fire.
In theory, it should help reduce the amount of attacks you get, and so have to return.
If you have friends on the same team, you can do art trades at any time so.

2) set a time/amount limit for yourself.
When I sit down to draw I can get lost drawing for hours and then put strain on my wrist when I knock out like, 5 drawings in a day, then can't draw for a few days, so I'm putting in place a time limit for each day. So I don't overdo it. eg maybe: 1 a week, or 1 a day. or 1 every 2 days? let people know in your bio? So they can't get salty about it when revenges are late or don't end up happening due to getting inundated and overwhelmed. I think mental/physical health should take priority always, and I don't see why people won't respect that, but it helps to let people know.

3) If I get more attacks than I can keep up with, I am going to try to prioritise first time attacks over chain revenge attacks. So most folk get something, over nothing and another getting a lot.
So if needed, narrowing the 'revenge priority' to 'first time revenge priority'.

4) just putting up a disclaimer that there's a chance not everyone will get a revenge attack because you don't want to burn out. Again I don't see why folk won't appreciate/understand that. Some folk attack more so to gift, than to get. But again letting people know your not going to run yourself to exhaustion and return all of them- could be good. I have a friend who starts each art fight returning attacks she missed the following year- which, i mean you could also do. But she typically seems exhausted at the beginning of art fight each year- and never seems to catch up entirely.

5) Smaller attacks over bigger attacks. I guess it is different for everyone- which I guess comm type/style is easiest for them. But if you start to get swamped, or even just as a principal to start. Do art that is easy for you. If I start getting swamped I think i'll scale down from fullbodies/halfbodies to just headshot attacks :3 But my personal goal is to do some sort of background ish thing for each. So scaling down won't hurt that a lot for me.