This is an experiment in the works.
There are two ways (probably more, but this should suffice for now) to loop record in Reaper.
1. Method 1: presented by Kenny Gioia in his Youtube tutorial, see below.
https://www.youtube.com/watch?v=lX9tv-h_stM
I hope I copied his custom actions correctly. Please feel free to make corrections and update accordingly.
Please find a custom keycap file that should contain all the actions you need.

2. Method 2: suggested by Chris G on the Reaper list. Steps below:
- create a new track (Control+t, Command+t on Mac).
- insert a new empty item using the "insert" menu.
- arm the track and turn on "normal" for track monitoring (F7 and F8 respectively).
- select some time, say from bar 1 to bar 3, then press control+r (command+r on Mac) to turn on "repeat mode".
- use alt+backslash (option+backslash on Mac) to rotor to the "auto-punch for time selection" mode.
- select the empty item, inserted earlier, and turn on the following "play all takes" and "SWS Set Monitor Track Media" options.
- set your tempo and whatever else before recording. At this stage hitting the "r" key should begin loop recording. At each iteration a new take will be recorded and the rest will be played as a stack.
- press the SPACE bar to stop recording.
- if you plan to do more work on takes, such as panning them or applying  various effects, I would recommend exploding those takes to separate tracks (there is an action to do that).
I have uploaded to this folder  a custom keycap that includes all the actions that can be activated with a single shortcut key.

Thanks and enjoy!
Vic