From what I understand, the Constitution does not forbid a sitting US Senator from being voted Speaker of the House
I think you are right. I don’t know of any part of the Constitution that says the Speaker must even be in Congress.
Good point. In fact, I don't think it even requires the Speaker of the House to have been elected to Congress.
Article 1. Section 2. ... The House of Representatives shall choose their Speaker and other Officers;...
While it's certainly reasonable to select one of their own members, I don't believe it requires it.
Yup.
The Members are free to nominate and elect any US Citizen, age permitting of course.
My choice would be former Florida Rep., and retired Lt. Col. Alan West, with permission to carry his loaded sidearm on the Floor of the House.