Hi here's a couple of ideas from the Logi manual (page 595 onwards):
1. "Audio recordings made in Logic Pro... automatically match the project tempo and will follow any
tempo changes made in the global Tempo track" - this is what's happening to you. The manual says this won't happen if you drag the files into a new project. Note: don't copy the regions across, but drag them from the finder.
2. Go to the Inspector for the region and uncheck the "Follow Tempo" box, if its checked. See if it makes a difference - i.e if you can change the tempo without the region changing speed.
Then, to get the new tempo, if your track has the same tempo all the way through, personally I would cut out a four bar loop, then use:
Options > Tempo > Adjust Tempo using Region Length and Locators
But try the beatmapping too, see what works best for you!