I think that is interesting. Of course, with any camera, it depends on what you are trying to shoot. I know you have talked about how birds are almost a matter of convenience, but, still, pretty amazing for where you live. Other than that, family and travel seem to be what you like to shoot.
With the RP, you would have fewer fps and MUCH less battery life.
For travel, the size/weight of the RP has to be appealing (if it wasn't for lens size, I'd consider it as a replacement for my M3/small kit). You can always travel with 2-3 batteries. But you would need to pair with some smaller lenses (EF 24-70 f/4, RF 35 f/1.8, etc).
For family, the AF point coverage of ~80% of your screen area would be great.
Looking at DXOMark, the measured sensor performance of the 6DII (assuming the RP is similar) and 5DIII are nearly identical, so sensor tech is a push.
https://www.dxomark.com/Cameras/Compare/Side-by-side/Canon-EOS-6D-Mark-II-versus-Canon-EOS-5D-Mark-III___1170_795
You go from not having 4k video to 4k video. No DPAF in liveview to DPAF for everything.
The low light AF is MUCH better on the RP vs the 5DIII.
Overall, my take on it would be if you want size/weight then the RP makes sense. If you want an "upgrade" really, the R would be more of an "upgrade" (sensor tech, etc).
What would probably interest me more is not having the RP replace the 5DIII, but augment it. Keep both and use the 5DIII when you want fps/battery life/and jury is out on AF speed and then use the RP for when you want size/weight, AF pt spread, low light AF, 4k video, etc.
As I know you really enjoyed the 5DS(R) the time you rented it, the question gets to be should you wait a year and get the high MP version of the EOS R, or pick up the RP now? The RP will likely always have the size advantage, so maybe you could have both in your future. The high MP EOS R will likely be equivalent or an upgrade to the 5DIII in everyway but maybe battery life.