With the benefit of hindsight, my biggest priority would be finding someone you (or they) can hire to help them around the house, at least a few days a week. In my experience, as they slow down they will let more and more housekeeping tasks slip, and when pressed will have plenty of rationalizations that they themselves believe "we'll do that later" "doesn't need to get done right now" "we don't use that enough for it to get dirty" etc. Someone coming in once or twice a week for 2-4 hours at a time will make sure those tasks get done, bring a spark of young person energy, and give them a cadence to their week (much more important for people living alone after their spouse has passed). It will also build a relationship with someone you/they can trust for later. This is perhaps easier said than done based on the stubbornness and that both of them are still alive, but I think this would have added the greatest quality of life to my own parents' end of lives.
Also I'm going to say that you haven't described much of an acute problem. Assisted living is a middleground, but that's a personal lifestyle choice and it appears they're deciding against it. By the time they're old enough to need help, they're past the point of assisted living, from what I understand. Having seen it, I would never want to go to a nursing home for my final days. Nursing homes are ugly end games that mostly exist because euthanasia is frowned upon and we don't want people dying in the street.
Other comments have touched on the legal stuff, but you want them to have Wills, DURABLE Power of Attorney, Health Care Proxy, and Living Will. Estate planning will depend on their/your level of wealth, whether you have siblings, and the state they live in. It's not just about divvying up their stuff when they pass, but is important for their own well being. Some of these documents need to be definitively in place now (Wills), whereas others the right time to have the conversation may be soon, or it may be after something significant happens to one of them. FWIW your Mom probably already has some rough expectations for what her life will look like after your Dad passes, if it ends up happening in that order.
Stepping back, you might just find that helping them at all is mostly impenetrable until one of them passes. And if that is the case, that is perfectly fine as well. It's more work when you finally do have to pick up the pieces and come from behind, but IMO you won't get anywhere by trying to force things ahead of time.