ReaPitch is crude. It's more of an old school pitch shift plugin meant to be used live and where the results - fidelity/artifact-wise - don't matter.
If you pitch shift in item properties, Reaper uses Elastique Pro. The classic linked pitch/time 'veri-speed' mode is truly lossless. The separated pitch or time adjustment (the 'DJ tricks' mode) lets you go pretty far and still sounds transparent.
So, you going for an authentic recording session tribute there by recording the coda section in a lower key and then pitching it up to match the rest of the song?