Hi everyone, I wanted to give you an update on what I decided.
So, I did move forward with the transmission replacement thinking that if it could get me at least four more years of not having a car payment, it would essentially pay for itself. However, that is not exactly how it turned out.
After getting the transmission replaced, I thought I should get the brakes checked out since that was one of the other things the dealer said needed to be done. Instead of the dealership, I took it to a mechanic that specializes in Minis and had relatively good reviews online. He took a look at the rear brakes and confirmed that they did need to be replaced.
However, upon further inspection, he was shocked to see that the rear calipers were almost entirely seized up on both rear wheels. This turned my $350 brake replacement job into a $1,200 brake/caliper replacement. Not wanting to essentially "waste" the transmission money I had just dumped into the car, I moved forward.
But things went from bad to worse. Once he replaced the brakes and calipers, he discovered that there was something in the brake lines that was essentially not letting the brakes release themselves once they had been engaged, creating a massive drag on the car. He surmised this was the real reason behind my transmission going out (the extra strain on driving a car around essentially with the brakes engaged at all times) as well as the three clutches I had gone through in the 82K miles I had driven it.
He replaced the brake lines, but it didn't solve the problem. He spent hours on the phone with Mini and other resources, to no avail. He donated quite a few hours pro-bono to the cause because it was killing him not knowing what was causing this issue. The next fix he could think of was replacing the ABS unit for another $1,000 plus, but couldn't guarantee that this was even the problem. I said enough is enough and drove it to a dealership as a trade-in the next day.
So, although I loved the Mini and how cute it was and how fun it was to drive, I will never buy one again and could not recommend anyone buy one, regardless of whether they have "improved" over the years. Still, I'm always a little sad when I see one drive by on the road.....