Also, I doubt Teddy would have pulled Wilson's OTL suppression of civil liberty and arresting of Socialists like Eugene Debs.
I wouldn't count on that. TR was ferociously hostile to "pacifists"
OTOH he might have attacked on a broader front. He criticised Wilson for prosecuting relatively poor men like Tom Watson, while sparing bigger fish like William Randolph Hearst.
(so when German u boats sink ships they aren’t American ones or even have Americans on them. Also tell Americans not to travel on British ships until the war is over. If they do that is on them individually).
The Vice President of the United States seems to have agreed with you.
On 11 May 1915 {ie just after the sinking of the
Lusitania) Thomas R Marshall made a speech in Tupelo, MS, in which he argued that Americans should think carefully before travelling on belligerent ships. Specifically "If a man goes onto an English ship he has in effect put himself on English soil, and should perhaps be willing to abide the consequences" [1]
This caused a bit of a flurry and some newspaper speculation about a rift between him and President Wilson. However, a few days later Marshall held a press conference at which he indignantly denied anything of the sort, insisting that he and the President were in complete accord. Make of that what you will.
[1] I don't have it in front of me so can't guarantee every word; but this was definitely the gist of it.