1997 Subaru Legacy Trouble shifting from 1st and 2nd (auto)

Two weeks ago, after being parked, I could not select reverse. Simply would not engage. Eventually did engage by driving forward (slowly) and selecting reverse. Following day it "popped-out" of reverse (with a thud) while I was reversing.

The following day that problem went away and has not reappeared. But a new problem surfaced. Now, when the car is dead cold (overnight, about 50 degrees F outside) it will not shift up from first. Stays there for about a minute of driving. When it finally shifts to second, it stays there way too long also. Evenutally, after about three minutes of driving, it goes to third, then easily to fourth. This pattern is VERY consistent -- does it every single morning. After that, no trouble at all until the next morning. Even after it sits at work (ten hours, maybe 70 F outside) all day it will shift fine at the end of the day. Only the mornings are an issue.

So far, no sign of the problem getting worse, or better, in over a week.

Added ATF (was low, but not too low). No change. Took it to a tranny shop, but because it was 'warm', it test drove OK. Not easy to leave it with them overnight.

It is obviously an old car with a lot of miles (but this is the first significant issue). I don't want to waste money on it unless it might be a relatively straightforward fix. From the description, can anyone tell what is happening? Huge thank-you for any advice.