@reginaldStjohn, yes, works okayish, as long as I do not have too many tempo variations and don't want to slow down or speed up. Seems to be the opposite of easy, at least without Melodyne.
I tried AudioSnap, put in quite some time to make sure enough important transients were good, meticulously corrected the clip's time map and created one okay version with the clip starting at the very beginning. Then I was foolish enough to try and move the clip and set the project tempo from the clip again. All damaged. And, even worse, the clip's time map is scambled. Also, a clip time map seemingly gets deleted when I save and reopen a project.
My current conclusion - I cannot use this. Whether it is me who is too stupid or AudioSnap, I cannot yet tell. Running out of patience, alas. I admit to being rather new to this DAW. But I am in IT all my life plus studied physics. I do understand the general problem, but not what this software does. I think I shall give up.
Thank you for your replies!