I don't understand why you think TR would be "harder" on the Allies (and presumably "softer" on Germany) than Wilson. If anything, I would think the opposite would be the case. "German surrender should be unconditional, he urged, dictated to the barking of machine guns, not the chattering of the President's private typewriter. The terms of peace should be severe..." https://books.google.com/books?id=pynyy2YCzwAC&pg=PA158 The US should not "pose as an umpire between our faithful and loyal friends and our treacherous and brutal enemies..." https://books.google.com/books?id=miuwAgAAQBAJ&pg=PT271 TR even objected to Wilson calling the US an "associated power" rather than an "ally" of the UK and France...
You raise valid points. I'd also point out that that was wartime rhetoric, and that TR was nothing if not practical. He had the credentials--street credibility, if you will--to arm-twist other negotiators to his views. They would have known they were dealing with a man who brokered peace once before and has the Nobel Prize to prove it.