I don’t know if this is going to be helpful, but I don’t use an automated BPM identification, I use different rhythm tracks (created in Audacity) till finding the matching one, and that lets me do posterior editing while keeping the beat on the whole timeline.
I don’t know but it’s not too hard to tap your foot and count for 30 seconds or a minute, and probably more accurate. (It’s easier if you count one- two-three-four, two- two-three- four, three-two-three-four, etc…)
Try the Audacity Limiter effect. It uses look-ahead to limit without changing the wave shape. Then as usual, make-up gain can be used to boost the overall loudness after limiting. But you might need compression or saturation to get a “fat” sound.