This is less for you and more for everyone else. I was in a very similar situation last summer. Row home, multi-level roof, a ton of tar everywhere, and a noticeable sag in the roof with leaking upstairs ceilings.

Ended up going with TSW roofers. I don't know anything about this stuff and had to research, but they were definitely not the lowest quote. Went with them because the methods and materials seemed better. EPDM membrane, all new plywood, plywood on walls and eaves, aluminum capping on perimeter walls (it's an end unit). Also made the choice based on vibes if I'm being honest. Not a very solid basis for a decision but I had a better feeling about them. Quote was $20k.

Anyway, Brandon from TSW noted the sag and made it clear we wouldn't know the extent of the damage until the roof came off, and there would be additional charges if the joists needed replacement. He said the roof felt solid despite the sag, and it's okay for them to sag a bit, but there was no way to know how bad it was. Makes sense, no choice but to agree.

They got the job done in three days. I'm struggling to remember the damage they found under the roof but it turned out not to be as bad as we were bracing for. Ended up paying an additional $3,000 for the hidden damage under the roof. Brandon texted me photos of the roof in real time to explain what was going on and what needed replacement. Definitely did not try to extort me when I had no roof and made sure I understood what I was paying for.

The thing that really assured me they were good is that my neighbor is a contractor and he can see my roof from his home office. As the crew was clearing out after finishing the job, I overheard him outside telling the crew how great the roof looked and what a great job they'd done. He didn't know I was eavesdropping. The next time he saw me he said "I can tell that roof wasn't cheap."

Should probably post this as a yelp review or something. I wouldn't hesitate to recommend TSW. There were other good things about them too (very respectful of our neighbors property, return visits to check on something I thought might be an issue) but you get the picture. Putting a new roof on an old house was the last thing I wanted to deal with and they made it as painless as they possibly could.