I can't perform in my current senior role so it's a bit of a tricky
Before we get to the actual answer, please talk to your boss first, and make sure that it's actually the case. Feeling like you undeliver, even though you may be performing fine, is very common, so it may just be that even your current, less productive, state is still at least on par.
But for purpose of the rest of this answer, I'll assume that it is as you stated.
Do you think it would be a bad idea to propose this to my current
I don't think it is a bad idea to talk with your boss about your performance, it is certainly better to be proactive and address the issue yourself, before consequences of it will catch up with you. This usually leaves a lot more place to maneuver between you and your boss, unlike when it gets to the point where you are invited for "the talk".
But I wouldn't frame it as suggestion to get a demotion. Instead I would explain your worries about the performance, stresses and troubles of your life and see what he says about it. If he agrees that the performance is not where it must be for that role, then you can negotiate some way to revisit your relationship in a way that makes sense for everyone. This can mean demotion, but it can also mean other arrangements - like keeping the title and salary but having reduced hours. Key is to keep the discussion open and be receptive to other side goals, as much as your owns. In the wise words of Alf: there is more than one way to skin a cat.
I'm conflict averse so I could just leave before I'm done probation
This doesn't have to be a conflict, and usually getting the jump on the issue makes the situation a lot less tense than it would be if you let it simmer.
What worries me is that you are still on probation, which usually means that you can be fired with very little, if any, cause and notice. Is that something you can afford to do right now? If not, I would not bring this matter at all, instead foucus on finding another opportunity, and only then either bring the issue up with current boss, or simply move on somewhere else. I don't know your circumstances, so I cannot tell you which one of those is the best, but you certainly must make sure that your well being comes first, even if that means you will be delivering sub par work while looking for another opportunity, and
I highly do not recommend for you to risk the income unless you are absolutely certain that you can afford it for extended period of time. More so as it's always easier to find a new job while you still have one, and current market is very uncertain.