Well, I'm tentatively considering Elihu Root for the former (largely based on Whan's posts in the prev thread).
Now that's something I haven't thought of or come across before -- I like it
Interesting... so, if I understand correctly, this could prevent Japanese militarism in the Pacific, and if Hitler's rise is also brushed out, a Wood Presidency could butterfly away WWII all together.
Now this is interesting... What about the economy? Does the GD still happen?
TR dies in Jan 1919, a year before the election. Despite our modern perceptions, he has been a very sick man since 1912, catching malaria and getting a serious infection, not to mention getting shot. I am not one to think that Dates of Death cannot change in AH, but unless you stop him from going to South America in 1912, he will get sick and be sickly and die a premature death.
Root or Hughes are both excellent statesmen from which to choose and both should be respected and considered. Root was pushing it in age too though. He did live to his 90s OTL, but he didn't know he would at the time. That's probably why Hughes was chosen OTL.
President Wood could have strong unintended butterflies with respect to WWII, especially Japan. The Hitler question would be difficult. The Washington Naval Conference would probably cause the biggest change.
Also, the GD will still happen pretty much OTL with a Republican, only semi-progressive 20s, no matter the president. Also, if Hoover is Sec of Commerce then expect things to go very OTL. He was a national figure as SecCommerce, known throughout America and a real go-getter. The only real things that could soften the blow of the GD would be if the US steps away from the gold standard (unlikely) or if there if farm relief is greater under Wood, somehow don't know what specific change could make it so.
Another way to stop the initial damage of the GD would have to wait until the President elected in 1928. Hoover negotiated with labor leaders and industries to not have a drop in wages which seems like a good idea but what that meant was greater rates of layoffs and less hiring since they could not change the worker's wages to reflect economic realities.
I am not sure if Wood was as a strong federalist as Coolidge or Hoover, which is considered a contributing factor to why they did little to regulate the economy as Presidents. Wood, being an Army man, may believe in a stronger central government and may be more willing to intervene economically. But it could go this was - Wood, as an Army man, defers economic decisions to the economic experts (aka Hoover and Mellon for the most part) so things go as they did IOTL. Mellon really did set the low tax standard that was the Roaring Twenties, and if he is part of the Wood administration, expect that not to change.
With respect to non-economic domestic policy, both Coolidge and Harding were fairly ahead of their times race relations wise, with Harding passing an anti-lynching bill. Harding passed the first major social welfare program with the Sheppard-Towner Maternity Act. Harding freed Debbs from prison, I do not see Wood doing that. He hated Commies.
EDIT: DID not see the Jr. on the back of TR! D'oh! He is far too green to serve as the real Sec of State. Maybe assistant of Navy as he was OTL, or War or State but he wouldn't cut the mustard for the top one. If Wood is President though, there is no Tea Pot Dome Scandal and therefore Jr's image isn't tarnished as it was IOTL.