I memorize chord progressions in terms of interval-number. E.g. {F# m; B dom7; E Maj} becomes {ii; V7; I}. I've memorized which intervals are major chords and which intervals are minor chords. So if I can figure out the tonic, then I can figure out the key. And if I figure out the key, I need only remember a pattern of ordinals (modulo non-triads).
This is a great illustration of how we grapple with the abstraction of scales and key over time.
First, you have tabs, which describe the physical position of the notes on the instrument.
Then, we have root / chord type notation, in which we describe the starting position and shape of the notes on the instrument, and the musician must translate that information to the physical position of the notes, on the fly.
What is important about this second stage is that the musician has a pretty good grasp on how to play, and can usually sight read a piece and get a pretty decent version of it just by tracking chords, or in the case of the piano, just chords and the melody on the other hand, or a small pattern.
Finally, we come to roman numeral notation, which describes the chords based on their relative position to the root note of key, not the chord. This is a powerful abstraction. It provides incredible insight into the relationships between music, notes, chords, and progressions of chords at a level divorced from the 'root' of that key. A 9th played over a minor 7th chord is going to give you a very similar sound in any key. This is a great skill for songwriters and composers, who need to have a strong working intuition about things like what chord will sound good in this progression, or what notes we want to appear in our melody (which is related to the chords beneath it).
