Have you managed to get your watch paired? I am facing a similiar issue with an Apple Watch Series 4 running watchOS 6.1.1 (stable) with an iPhone SE 13.4.1 and 13.4.5 (beta). The behavior is exactly the one you are describing.
It is still possible to achieve the same settings that "watchOS6Seed1-compat.mobileconfig" is doing:
a) set back your phone date to a date prior to October 12, 2019 - this will install the profile.
There is one downside however: If you need to communicate via SSL to any server it will most likely fail due to invalid certificates. So assuming that profile would allow you to connect to your Watch, you'd probably have trouble actually activating or updating the Watch because the iPhone cannot communicate with any SSL servers.
b) use a j*ilbreak. I will not provide any files, just the way:
1. download "watchOS6Seed1-compat.mobileconfig" from known sources to your Mac.
2. set back date to October 10, 2019
3. AirDrop the file to your iPhone or upload it to an HTTP (not HTTPS) server and download it from your phone
4. Install the profile and reboot
5. j*ilbreak your device.
6. Install Cyd*a and OpenSSH.
7. connect to your iPhone via SFTP and go to /private/var/Managed Preferences/mobile/ and download file .GlobalPreferences.plist
8. check the contents of .GlobalPreferences.plist : it should contain EnableNRBTLMBackwardsCompatibility = 1; (this is the setting the profile is actually making to your iPhone)
9. set back date/time to today
10. notice that the profile gets deleted automatically and also the .GlobalPreferences.plist was modified again.
11. Now upload the previously saved .GlobalPreferences.plist including the setting back to your phone.
12. Restart (may or not be necessary - I don't know)
Now you should have the same effect as you'd have after having installed the profile only with the important difference that SSL communication is not broken, assuming that the setting in question still has effect in new iOS versions.
However in my case it didn't help - still cannot pair the Watch. But maybe somebody else will benefit from this.