I had to have new units installed 5 years ago. The original system used the old refrigerant so the entire system had to be changed out. Got new Carrier heat pumps for both floors. Cost ~$10K. I had 4 estimates and chose the company with the best reputation, not the cheapest.
You did it exactly right.
I went through the same thing during the pandemic, July 2020. Mine unfortunately was 50% more than yours.
People in the business or who can DIY are going to insist I got mugged, but let me tell you, they wanted $21k. lol
But what's critical about your post--you don't want the cheapest quote. You want the best job (often higher quotes), but the cheapest price.
In my case, the cheapest quote omitted the chimney liner (when a high efficiency furnace replaces the old 78% one, the water heater is orphaned and now there's not enough heat to prevent condensation which will destroy a chimney over time). I googled and that can be a $2k standalone job.
My price was also higher imho because the system is a TRANE.
Also, I got 0% for 60 mos, equal payments, not to be confused with 0% minimal payments. My buddy lectured me since he's a fan of DR, you can't pay cash, you don't get it. But it's 0% equal payments, same price as if cash. But nothing, and on and on (he didn't do what he said and claims well he's in Jacksonville he can't do without AC like I could in PA, always excuses).
But again, I dare say you hit the nail on the head, you don't want the cheapest, but the best job, often that's reputation.
I noticed that many did not push the 94%-96% furnace--why would they not push something more expensive? My guess? The chimney liner, and less margin as more labor drilling through the foundation for the intake and exhaust. Anytime a vendor doesn't push a more expensive product, that we are interested in, is a red flag.