As someone working on anima #4, I have two things to say on the matter:

1) It's better when it's current. In this late stage, you're feeling that grind all at once, and that can definitely cause issues. After doing animas both incrementally with each patch as well as grinding it all in one go, I'm glad that my first animas I did with each patch when the grind wasn't as big of a ordeal. It's a good lesson for when the relics come out in Stormblood.

2) Sometimes it's more than just burnout. Right now, I'm on my aether phase for a DRK relic, and I'm sure it might stay that way even into Stormblood. Although the burnout is real, it's not the major reason why I've mostly stopped working on it. The biggest reason is primarily the whole a1s PF demand for as few tanks and healers as possible, even seeing a couple of 1 heal/7 dps groups, meaning that as a tank or healer, it's unfortunately a lot rougher and at this point in the game, it's just not worth it for a job I probably won't play in Stormblood. Looking back on it now, I'm actually surprised I managed to get my SCH relic done because of it.

Best tip I can give to the OP? Throw your relic away. Hide it on some retainer. Do anything you can to make you stop caring about it, because all it's going to be in a couple months is a glamour.