In your situation, I don't think I would recommend it. You have enough on your plate. Harnessing requires not only the proper type of harness (many unsafe ones are sold), but it needs to be fitted properly and the rabbit needs to get used to it over a period of time. Not all rabbits will take to it.
There are also many risks associated with harnessing improperly. With your claims of often forgetting basic tasks, the idea of forgetting something during harnessing training or attempting to take bun outside with one, just isn't worth the risk, imo.