As we all know, there are good reasons for two-season progressive leagues (that is leagues in which two seasons' players are drafted and used on rosters, with the two seasons advancing one year at a time - say 1914/1964, then on to 1915/65 etc.):
Until 1962 there are fewer than 24 teams and in WIS baseball leagues anything under 24 teams excludes a wildcard position. This means that at most 4 teams, and with 16 teams only 2 teams advance to the post season.
So the dual-season structure enables a larger size league, more playoff spots and therefore more chances to make the postseason, which in turn makes the league more attractive to join.
There is, of course, a downside - drawing from 32 teams for a 24 team league means that about one full league's worth of players (8 full teams' worth of roster names) are not needed and so only the best 24 teams' worth are drafted, leading to the undesired-by-many of us effect of having "All Star Teams" (Henry Aaron in left, Babe Ruth in RF etc.).
Dual season progs may not be ideal, but they do have the advantage of being "What if" leagues in the sense that one can find out how Tom Seaver does pitching against Ty Cobb, but outside of the baggage that comes with being in OLs.
I think there are ways in which we can have dual season progs without the All-star effect. It requires deciding that the league would be a sort of hybrid, in which a preference for one era over the other would be an operating principle. In other words, we will play the 1910s and 1950s but we are more interested in the 1950s.
So we will take all 16 teams from the 1950s but only 8 teams' players from the 1910s. In other words, 24 teams worth of players will end up in a league of 24 teams.
This means we have several options on how to decide which players from the 1910s to use:
1) Only one league - AL or NL excluding the other for the length of the progressive league's existence
2) Only one league at a time - this would enable a league to begin at an earlier date - say the 1930s instead of the 1950s, with the second time period being say the 1900s on, but using only the NL team rosters from 1900 to 1929, then, having begun the league in 1930, and playing through 1959, the league could play 1960 with the AL team rosters from 1900, so that by 1989 the second source of players were the AL rosters from 1929. In this way the league avoid having players repeat their existence (taking out the occasional individual player that played for a couple of decades).
3) Using players from both the AL and NL teams from the second (earlier or later) time period but using only half of those rosters - either the bottom 8 teams in W-L record overall (for example teams 9-16 from 1904:
http://www.baseball-reference.com/leagues/MLB/1904-standings.shtml ) which would include some stars and even superstars but by definition not include above average overall rosters and players as a whole, making the All-star team effect even less likely) or the best 8 (if it were desired to have many of the best stars from that era play in the progressive league precisely to have the Willie Mays v. Walter Johnson what if? thing happen), or by any other criteria the league owners choose to use. Anyway, some ideas to consider.