Does Apple Music for Windows support the iTunes Remote app?

I have been experiencing major issues with my iTunes app in Windows 10 Home (as discussed earlier). I essentially had no choice but to upgrade to Apple Music. Now I cannot get Remote to work from my iPhone.

I did call support yesterday with no success. My Apple support rep was not aware of the Remote app, claiming it was third party.

I cannot use remote desktop, as I have the Home version, and was not able to upgrade my computer (following two attempts).

Going to a different service is not feasible with more than 30,000 songs in my library.

I did see a possible but not inexpensive solution with Apple TV. Are there any other ideas to get my iPhone to control my home system?