As a former shop owner this is a tough situation. Most shops will offer a "free fit" if you buy the bike from them, but it's the "free alignment when you buy tires" kind of thing. It probably won't be comprehensive, unless you're buying a bike that has the kind of gross margin needed to cover a 2-4 hour long fit session. If they did that for every bike on the floor it wouldn't be good for them.

On the other hand knee angle is only one aspect of fit. Reach, as you pointed out, is important as well. My expectation of a reasonable shop is that they do a very rough reach type check. If you need to get a different stem it might be a take-off from another bike or you may need to pay a reduced amount for a stem.

An experienced fitter will get 90-95% of the fit just by eyeballing the rider on the bike, at least that's what I found. There are minor things that are hard to eyeball, like cleat position on clipless pedals, but saddle height and bar reach should be pretty instinctive for an experienced fitter.

Finally keep in mind that fit is relative to rider fitness. As you ride more and more you'll develop those muscles that allow you to hold what is usually considered to be a more aggressive position. Remember that pros, for all the "racing" that they have to do, ride their bikes more than most of us, in the 20k miles a year range. If they weren't comfortable they wouldn't use their position. As radical or extreme as their positions might seem they're acclimated to them and in fact I bet that if you made some arbitrary changes to their position to make them "more comfortable" (lower saddle, reduced reach, increased height) they'd be both upset as well as less comfortable.

This means that your "fit" right now may not be applicable in a few months. A good example of this is a friend and teammate of mine. He got the full blown professional fit at a shop. He was, at the time, a relatively new rider/racer. After a couple years he asked me for feedback on his position. I recommended radically changing his position, which he did a bit hesitantly. After the fit he won three midweek races (he'd never won them before) and he placed 3rd in a season long target race. Since his fitness didn't change between one Tuesday and another it was really down to the fit. It enabled him to put more power to the pedals, be more aero, and yet still be very comfortable if not more so.