When you downgraded, did you COMPLETELY ERASE the internal drive first?
If the answer is "no", I'm thinking that's got something to do with it.
What you could try:
1. Get an external hard drive
2. Get CarbonCopyCloner (FREE to download and use for 30 days)
3. Use CCC to create a bootable cloned backup on the external drive
4. IMPORTANT: For this operation, DO NOT let CCC clone the existing recovery partition -- you want to "leave it behind".
5. DISCONNECT the backup, and now boot from your bootable USB flash drive
6. Open Disk Utility and in the View menu choose "show all devices".
7. Select the "topmost" line (representing the physical drive) and erase it to APFS, GUID partition format
8. Now close DU and reopen the installer. Do a clean install of Mojave, which should also install the correct recovery partition
9. When done, you will see the setup screen.
10. STOP RIGHT THERE and connect your external cloned backup.
11. Now begin setup. At the appropriate moment, setup assistant will ask if you wish to migrate from an older drive. YES, you want to do this.
12. "Point" setup assistant at the external drive. IT WILL TAKE A WHILE TO DIGEST THINGS. Be patient, you don't get much feedback while this is happening
13. Setup assistant will present you with "a list" of stuff to migrate. I suggest you just accept everything. Let setup assistant do its thing.
14. Be patient. When done, you should see the login display.
You should be "back where you started from" with Mojave as the boot OS and also on the recovery partition. Try it to be sure.
A bit of advice:
In the future, DO NOT ATTEMPT TO INSTALL BETA SOFTWARE on your main, working drive.
Instead, if you want to experiment (as I do myself), USE AN EXTERNAL DRIVE as your "experimental drive".
This leaves your main working OS untouched and... well... still working if you want to "go back" to it.