In trying to help my dad with his collection (not jazz), I've advised him to catalogue via discogs or spreadsheet and sell in bulk or at a record show (or both). Piecemealing them out either in an online market like discogs, other sites, or at auction takes a special individual which neither of us are.
I got the big early Basie/Prez set a few years back when it came out and somehow or other that particular set was so enjoyable that I started buying Mosaic sets in earnest. I had been buying them for decades but somehow with that Prez set the addiction kicked up a notch. I did a lot of shopping and bought scads of used sets. My Mosaic boom is just now cresting because most of the ones I don't have are either prohibitively expensive or I'm probably not that interested in the music; I'm getting to the end of my want list. I'm in my early seventies and acutely aware of the issue which occasioned the thread but I guess I want to glory for a little while in the physical possession of all these grail items. It's one of those "Lord make me chaste but not yet" types of situations. I'm getting on so I suppose in a year or two (or five) I will start doing the Swedish death cleaning I noticed the rents doing around this time of their life and get all systematic and at least sell off the box sets.
My understanding is that they were introduced at the same time as the 10" but were used mostly for classical pieces.
My understanding is that the 12" became the preferred size for all LPs somewhere in the mid 1950s. No hard cutoff date that I can find, just product/consumer evolution.
https://en.wikipedia.org/wiki/LP_record