I took a look at the most recent log you provided, and I notice that you're running the Duo Authentication Proxy on the same server as NPS/RRAS. While this configuration is technically possible, it's more difficult to troubleshoot issues with the configuration because many of the tools we'd normally use (like a packet capture) don't apply to localhost requests.
In the log you sent, I too observed four unique incoming RADIUS authentication requests from 127.0.0.1 for the same user within 9 seconds, with no waiting for an access accept or access reject response from the proxy before initiating the next one. Duo isn't initiating spurious approval requests, it's responding once to each of the four unique requests sent to it by RRAS/NPS (which in turn may indicate unique requests from the VPN client to RRAS).
The first thing I'd check is the RADIUS server timeout in RRAS, to ensure it is set to 60 seconds the lifetime of a Duo push request). I think you already confirmed it was, right?
If you append a Duo Mobile generated passcode to your password during VPN login (like password123,123456), then are you connected immediately?
Gabby will reach out to you again to continue working on your open case with some additional suggestions.
Thanks for trying Duo!