Your post-1930 analysis strikes me as very sound.
However, I am not so sure that I see that:
the center-right was already the dominant force in the Republicans by 1896.
The Spanish-American war does not strike me as conservative, and Theodore Roosevelt doesn’t seem to me conservative at all. That Roosevelt was able to strip so much support away from Taft, a sitting president, and carry a higher percentage of the vote than Taft (who finished 3rd, four percentage points behind Roosevelt) says to me that the centre-right was not yet dominant.
Well, with the capture of the Democrats by the left in 1896 under Bryan, it was William McKinley who offered the country a continuation of center-right normalcy, closer in style to the outgoing Cleveland Administration. Theodore Roosevelt wasn’t a national figure yet at that point. It was New Jersey political operative Garret Hobart who went on the ticket with McKinley that year.
The Republicans weren’t entirely unified with the business class that year, with many plains and mining state Silverite left-wingers splitting from the party and going with Bryan. The Cleveland Democrats (Pro-Gold) even put up a ticket of their own in 1896.
TR was elected Governor of NY as a Reformist in 1898 and attracted national attention. The GOP party bosses weren’t too happy with him (they never are with outsider reformists, look at the opposition to Trump). With VP Hobart’s death before the 1900 elections, they placed him on the ticket with the President (and becoming VP in those days was almost the political kiss of death), hoping that would deflate any ambitions and keep him quiet for the next 4 years. Only with McKinley’s assassination did that “nothingburger” VP job mean something again (repeating the same situation as a NY pol by the name of Arthur did following an OH pol named Garfield to the Presidency 20 years earlier).
TR didn’t really market himself as a left-winger, but as a reformist against the party bosses and big business types (he did explicitly blast the Socialist Democrats). Again, it was somewhat Trumpian-style Populism. Aspects of it at the time could be viewed as antithetical to Conservatism, but it wasn’t of the pinko variety, it was a new appeal to nationalism. As it was, TR only ran one successful Presidential race, that in 1904, against a moderate Democrat opponent from NY, Judge Alton B. Parker (Parker trying to walk a fine line by appealing to both the old Cleveland wing and the Bryan firebrands, the latter having come off 2 failed runs in a row).
TR expected William Howard Taft to continue his style of governance (Taft himself was not really a politician, 1908 being the first time he had run a race for office, the previous jobs all having been appointed, such as Cabinet and Governor-General of the Philippines). I got the impression he wanted Taft to be a puppet for his policies, since TR had stupidly (for him) chose not to run in 1908. When Taft started to chart his own course, TR resented him and set out to defeat him by any means.
It seemed like Taft was never able to get any traction of his own accord and get out from under TR’s dominating force of personality to become a strong political force in his own right. The 1912 GOP Convention was a brutal and ugly affair, described as the worst since 1872 when the pro- and anti-Grant forces split. You had 3 major candidates, TR representing his own faction, Taft, and from the far-left, WI’s Robert La Follette, Sr. Had the TR and La Follette factions been able to unite the center-left Progressive wings, Taft could’ve been deposed at the convention and even a battered Roosevelt might’ve been able to defeat NJ Gov. Wilson in the general.
As it was, with 2 Republicans going into the general election, Wilson was going to prevail with a plurality (similar to the 1992 election, with the Dem base holding for Clinton and Republicans splitting between Bush, Sr. and Perot). The combined total for Roosevelt and Taft was 50.6% with Wilson getting just 41.8% (lower than Clinton’s 43%). The split was almost right down the middle, with 23% going for Taft, 27% for Roosevelt. It had to be difficult, too, for regular Republican voters having to figure who to vote for as November approached, stick with the President or go with Roosevelt, who was closer to beating Wilson if he could pull away.
Still, for all the claimed popularity of TR, getting just over 27% was not exactly an affirmation of that. Worse yet, because the two parties also ran separate downballot tickets, it enabled the Democrats to win Congress with pluralities, and gave Wilson carte blanche to do his worst as a Socialist (and again, TR did consider himself to be to Wilson’s right).
Despite the fissure in the party, it was able to reunite within 2 cycles and only due to some mistakes on the part of centrist Charles Evans Hughes in 1916, came within an inch of dispatching Wilson (California being the key to the election in the Electoral College, which sadly went to the Dem).
With the Dems being toxic in 1920, whomever the GOP nominated that year was likely to win. Initially the race was between Gen. Leonard Wood (representing the former TR forces) and IL Gov. Frank O. Lowden (an old-line McKinleyite). Wood lacked political experience and Lowden might’ve taken it had he not been seen at the convention attempting to outright buy the nomination. That left the dark-horse Ohioan Harding, a Conservative, to get the nomination, and gave the GOP the largest margins in the modern era (outside the South, still one-party Dem), and Conservative dominance until the former Progressive Hoover blew it, leading to FDR and all that came after.
Just as one last aside, FDR ran to Hoover’s right in 1932 claiming to be a fiscal Conservative (a gargantuan falsehood, as it turned out to be). Ironically, had FDR employed the same tactics President Harding and Treasury Secretary Mellon employed in 1921 in ending the Wilson Recession of 1920, we’d have been out of the Depression before 1936. FDR, of course, exacerbated it, successfully blamed it all on the GOP (even into the ‘40s). It really took close to 20-24 years to recover from the economic damage. By then, of course, the GOP had slumped into a “me too” party, and the aforementioned statist and moribund entity.
One last comment, I consider President Harding to be one of the great Presidents, which counters that of many historians (left-leaning). Harding was the last President to date who cut taxes and spending/government size in order to hasten the end of the Wilson recession and boom of the 1920s. Leftist historians hate Harding because he proved quickly and easily that Conservative economics works and spectacularly so. He was fortunate to have Coolidge to continue those policies. The 1924 election, curiously, was the last time that both parties put up right-of-center nominees for President, to the horror of the left (GOPer Coolidge and former Wilson Solicitor-General and WV Congressman John W. Davis for the Dems). That was also the last time the GOP carried a lot of now-stalwart Dem areas (such as St. Paul, MN, Boston-Suffolk in MA and every single county in NY state, including all 5 NYC boroughs). The left put up their own party under the Progressive label, running the Republican Socialist nutter Sen. La Follette.