This is an excellent idea and I enjoyed the linked report at Dtdb.
The deck I played at GenCon 2018 with made the cut and had 32 cards from the base set: Sloane Town Square blitz is simple to play too! Some other factions might have a tougher time with a limited card pool than others. Could easily push this closer to 52 (54 including jokers!) base set cards by adjusting deeds/dudes/goods, but core strategy of the deck would be unaffected.
I think Law Dogs would find a "just base set" environment particularly tough as they were hamstrung with poor starting dudes for much of the AEG era. Clear from tournament results over the last year or so that Thunder Boy and Hattie rectified this. Fourth Ring would lose some of the complexity/toolbox that makes them powerful, but they'd still have Blood Curse and Hex Slingin' so they'd probably be alright!
I've advocated a 2x Base set, 1x Saddlebag, 1x Pinebox, 1x playset set of a specific card as an interesting handicapping experiment if people have different collection sizes or just want to experiment with a different environment. Expansions add excellent bullet catchers (base set lacks 1GR drifters) so any casualties hit you harder, plus starting posses are tougher for some factions/deck styles if they don't have Jake Smiley.
Look forward to seeing how your deck evolves as you add expansions at each event.