Since i started speed running this game i have discovered a couple things that can help YOU get your time down.

1. Keep clicking Runs are done on cakewalk difficulty so there isn't to much strategy involved in the runs so you do not need to use all of your stamina per turn or even visit to many states preferably you want the turn to end as soon as your opponent is done so don't spend to much time per turn doing things.
2. Endorsements The primary strategy I use when running this game is just to get enough endorsements. On cakewalk mode your opponent generally will not get any, so you can rely on only the endorsement bonus to carry you to victory.
3. Move as little as possible Moving in the game, especially flying from one end of the map to the other, takes a very long time. of course you have to move to do anything useful in the game like gaining endorsements which is important to my victory strategy. If you must move I recommend traveling to a bordering state to minimize travel time. I also like to stay in the North East when setting up outreach centers, because all those states are small and close together which is good.
4. Stamina When running non custom candidate category's its important to choose an opponent with very low stamina (example Joe Biden has 4 stamina) this should cause your opponent to not be able to travel as much, which in theory should make the turns shorter.
5. "Credits Warp" There is a glitch in this game that i have dubbed the "Credits Warp" which allows you to completely skip the electoral college count, which shaves about 30 seconds from your run. This of course is incredibly useful the ways i have got it to work is simply click really fast on the next button the last turn of the game, on my computer at least this causes the game to lag and will send you to the concession screen, after you are on the concession screen you click the "view map" button and the game should correct itself and take you to the victory screen. the only weird part is that your candidate will still be looking down as if they lost but also jump like they won. For examples of this check out my runs.