Something I have never seen, but I have toyed with the idea, is bundling players into groups. It would be a little more upfront work for the commissioner, but would radically shorten the draft.
For example, say you're starting with a 16 team league, some season prior to expansion. You might select a group of about 96 or 112 players (6 or 7 rounds worth) that would comprise the draft pool. All other players would be grouped into bundles, ideally with a relatively even distribution of position players, pitchers, etc. Those bundles would be selected as a group. You could stick the parks in the bundles too.
So say we're doing 1946...it's an 8 round draft. Each owner will pick 7 individual players (drawn from the 112 that you set aside...this would be Musial, Williams, Spahn, Feller, etc.). And each owner will pick one bundle, to be used to fill out their roster. Yes, some bundles might be better than others, so you might want to select one earlier in the draft.