I go from BIAB to Reaper all the time. There are a few (fortunately simple) things you have to do to make everything work.

First, before you import anything into Reaper, make sure Reaper is set to the same BPM as the song in BIAB. Also make sure the time signatures match.

Second, once you have everything imported, select all the BIAB track items, then right-click on one of them to get Reaper's context menu. Under Properties (not Item Properties or Source Properties), go to Playrate, and then click Reset Playrate. This will shrink/stretch all of the .WAVs to where they should be.

Best,
Tom Smith
Win10/64 • i7-8700K • 24 GB RAM
BIAB 2025 • Reaper 7 • Izotope MPS
AKG C1000S • IK iRig I/O Pro