A little late to the discussion but I just went through the process with Chrysler Capital and so I thought adding that experience could be helpful.
We wanted to buy out our 2020 Ram 1500 Laramie - truck is loaded and about 60 days before lease end, the dealer started calling / emailing. No surprise there. Just ignore them.
I called Chrysler Capital in mid September, said I wanted to buy the truck. First answer was "work with the dealer." I explained our dealer's finance department was awful and kept us waiting for about 2.5 hours to even start the process, when we had made an appointment for a time convenient for them. They listened and I said, "can't I just send you a check for $34k and buy the truck?" They relented and said "sure."
They then sent an odometer disclosure statement - I filled that out and sent it back. They then sent the buyout figure, which matched the lease exactly (you never know).
Then my wife and I discussed options - pay cash or finance. We were offered a 4.7% rate through the credit union, and my personal .02 was that I would always rather use someone else's relatively low rate money than our cash, particularly when we are in a 3 plus percent inflationary environment, which means in reality that 4.7 rate is really sub 2 percent. Went through the process with the credit union. They approved us and sent a check to Chrysler Capital. First hitch in the process: Chrysler Capital (despite the credit union asking them NOT to do this), sent the credit union the title and made out the bill of sale to the credit union. So that needed to be corrected - had to get the credit union on the phone with a representative from Chrysler Capital so that CC could get authorization to have the bill of sale indicate that my wife and I were the buyers. The credit union also mailed me the title and lien on title that CC had sent to them.
Showed up at DMV, was told lease buyouts were "tricky" but we had what we needed and were out the door within about an hour.
If I were going to do this again, I would have the bank / credit union make me the check, and I would mail to CC. CC told us they don't make out titles to someone other than the payor of the buyout figure, but that is kind of screwy since I am going to guess a lot of people use banks/finance companies and banks don't want the title to the car, they want your money (and the lien until they are paid).
But overall it went pretty well, and I never called or spoke to anyone at the dealer. Hope the experience is helpful to others.