Thinking on the 1920 election,
We know Frank Lowden is going to be the hapless Liberal, he straddles the old-guard/moderate line, is amendable to both Eastern finance and Midwestern/Western agriculture, a perfectly fine candidate in normal times after four years of Root he's going to be on the wrong end of a landslide.
It also means every Democrat and their mother is going to be running for the 1920s nomination, and we also know that after three runs of Hearst and another of McClellan, New York's Democrats have had their time in the sun, but if Democrats can't get NY's 63 EVs, they'll at least have to get Ohio's 32. So the party's candidate needs to run strongly in the Midwest.
Logically that would means the next nominee would be steered to either the number 2 man on McClellan's ticket, the Senator from Ohio, Newton D. Baker or the state's Governor James M. Cox. Baker is the well-spoken protege of Hearst's old Veep Tom Johnson, a Georgist, and a progressive in the Jeffersonian mold. OTL the much talked about stop-FDR candidate at the 1932 DNC, here he's the logical pick for a Democratic convention, as an eloquent orator from a key swing state, who's broadly amendable to the party at large (his support for the LoN which brought him Bill Hearst's ire OTL is presumably a non-issue here). What's stopping him from becoming the runaway front-runner is a historic disinterest in the job, which keeps him from becoming an overwhelming favorite and may lead to him pre-emptively withdrawing in favor of...
Governor James M. Cox, the OTL Democratic nominee in 1920. Fan of labor, progressives, Americanization, and Roosevelt. He shares much the same niche as Newton Baker but has shown greater interest in the Presidency. As a proven vote-getter in the Buckeye state that makes him both an attractive candidate and a broadly amenable figure to the ex-Populists in the Heartland, the Tammanies in the East, and the Progressives in between and out West.
Outside of the two Ohio men, there's the Plains/the Heartland/Flyover country, hater of monopoly, and railroad companies, lovers of farmers, farm subsidies, and price supports. Home to the ex-Populists of the Weaver-Bryanite tradition, bad blood from Bryan's role in attempting to usurp the man from the Empire State in 12' and in keeping the White House from Adlai the 1st in 00' likely going to prove as much of an obstacle to one of their candidates winning the nomination as much as their fear of and rivalry with the Tammanies out east.
Gilbert Hitchcock, Senator from Nebraska, and Bryan's old protege is likely to make a go of it, running firmly in the Populist tradition of the Boy Orator, he may be joined by Senator Thomas Walsh, Montana's Catholic Senator, who's ties with Labor, Progressives, and Suffragists, would make him a very attractive candidate if he came from state that could call upon more then 5 electoral votes. Their showing on the balloting will be there, but their path to the nomination is narrow enough without the Democrats from the Empire State distracted by internal feuding.
Champ Clark, is also likely to make a go of it, as Speaker of the House and one of the grand old men in the Democratic Party. Mostly acceptable to all it's wings, he runs into the problem of being 70 when the Democratic National Convention meets to select it's nominee and with a party filled with young blood itching to move forward past the Hearst and Hughes and Root years, I think his political half-life has passed him by.
Otherwise there's probably James Gerard as Tammany's favorite son. New Yorker's have had four bites of the apple, they aren't getting a 5th. Plus a broad smattering of favorite sons, including the Sinophobic Senators from the Pacific, and representatives of the Eastern states which are not the Empire state. Plus one or two men on horseback hoping that a chest full of stars will be a ticket to Lemon Hill and the Square Kilometer.
I'd be surprised if the party's next nominee and by extension the next President comes from outside the Buckeye state, I'd be very surprised if they came from outside the Midwest.