I know one car is an exempt asset for Medicaid purposes, but how are jointly owned cars treated with respect to Medicaid?

I take care of my father who has Parkinson's disease and dementia. He sold his house not too long ago and currently lives at my house. I use a nearby ALF for respite stays and adult day care periodically. This works for us right now, but he may make this ALF his permanent residence in the near future. If and when he makes the ALF his permanent residence, he will likely run out of money within 3 years. If and when he moves to the ALF, I will still be his advocate and part of his care team. I will continue to take him to his doctors that we have established a relationship with over the years as they would not be able to come to the ALF. My father has not been driving for about 8 months now and his license is up for renewal in a few months. We were planning on letting his license expire. Originally, he had 2 cars titled to his name and insured by him. Car #1 was the car he used and car #2 is the car I've been using for the past 10 years. Car #2 was my 1st car and purchased for me as a gift, however the title remained in my father's name all these years. We sold car #1 a few months back as it was not being driven. Car #2 is still being maintained and used by me to this day. It's worth maybe 2-3K at most. With my father's license up for renewal and ALF permanent residency on the horizon, I wanted to make sure I planned accordingly and had a couple different ideas for what to do with car #2. Idea #1: Leave everything as-is with car #2 titled and insured to my father. I will continue to keep the car at my residence and maintain and use it. My concern about this is, I'm not sure if he's able to insure the vehicle once he moves to ALF as he won't have a drivers license and the car won't be stored at his ALF residence. Idea #2: Transfer the car title into my name as a "gift" and then insure the car myself. Even though the car was technically gifted over 10 years ago, I assume Medicaid would still look at the transfer as a gift. If they did, is this easily resolved by paying the fair market value of the car at the time of medicaid application? Or is it not worth the potential headache later? Idea #3: Transfer the car title into my name and pay my father fair market value of the car avoiding any potential medicaid issues later. I would prefer not to have to put any more money into this car as the reliability of it is questionable at its age, but I suppose this is probably the safest option? I would then insure the car myself. Creative, but possibly risky idea #4: Have my father trade in car #2 towards a minivan that we title jointly - I could pay 50%, and my father could pay for the other 50%. Then I would insure the car myself. I wouldn't be able to afford it at 100% ownership. Could this be considered a legitimate spend down of his assets? Car #2 works for us, but it is very compact and is tough for my father to get in and out of. My father is still mobile, but a minivan would definitely be help us mutually now and even more so in the future if and when his mobility is lost. Would something like this be scrutinized and is it worth the risk? Idea #5: ??? I've found this forum to be tremendously helpful. Any thoughts/suggestions are greatly appreciated.