As discussed elsewhere on this forum, Reaper (at its current version 6.81) will not follow Midronome's MIDI clock in realtime while recording a tempo-varying performance. However, once the performance has been recorded, it is possible to make Reaper's internal clock (and thus its MIDI beat grid) adopt the performance's tempo variances for all subsequent edits and overdubs.
You need the SWS extensions set installed for this as well as an audio interface connected to the analog clock output on the back of the Midronome.
1. Set project timebase to "Time" and choose a nominal tempo and time signature, e.g. 120 & 4/4. Disable Reaper's internal metronome.
2. Create tracks to simultaneously record:
- Midronome's analog clock output (click track) as audio
- Your performance as MIDI on one or more tracks
- Optionally, your performance as audio
4. Record your performance using Midronome to vary the tempo, listening to Midronome's click audio as needed, either from the jacks on the back, or from record-monitoring the analog clock click track in Reaper, or (better) latency-free directly through the audio interface if it supports that.
5. For all of the performance MIDI tracks, under Source Properties select "Ignore project tempo" and use your nominal tempo and time (120 & 4/4). This will keep the MIDI from getting remapped to the tempo markers we're about to create in the next three steps.
6. Select the click track audio media item, right-click and do "Item processing" > "Dynamic split items… " Select split points "at transients" and action "Add stretch markers to selected items." Adjust other parameters as necessary so you end up with one Stretch Marker on top of each click pulse and no extras in between.
7. From the Actions menu, run action "SWS/BR: Create project markers from stretch markers in selected items." You should now see a whole bunch of (red) project marker lines, one on each beat, aligned with the pulses in the click track.
8. From the Actions menu, run action "SWS/BR Convert project markers to tempo markers" with default settings: bars of 1/4, gradual changes, remove project markers, click convert.
[Note: I don't know if there is an internal limit to the number of project markers, but this will create one for every beat of the performance, so that's potentially a very large number. Might need to split the click track into chunks and do these last three steps on each chunk individually.]
9. For all of the performance MIDI tracks, do "Glue Item" to replace their internal 120-&-4/4 grids with the new project varying-tempo grid.
10. Optionally, view Reaper's tempo envelope track and make any desired adjustments to the tempo variances or add time signature markers. (If you do this, you may want to change the time base of any performance audio tracks from "Time" to "Beats" and use stretch points to shift small segments of the recorded audio to keep them in alignment with the adjusted tempo markers.)
11. Record additional overdubs as desired, hereafter using Reaper's metronome click instead of Midronome's. USB MIDI output devices should once again have "Send MIDI Clock" turned on.
Note: If you want to have multiple independent/uncoordinated tempo grids running at the same time, Reaper's "subprojects" feature will let you achieve that.