Hello midnight_doom,
You're correct that signing in to another Apple ID in iTunes, may result in not being able to switch accounts for the 90 days, as described in this message.
To back track a bit, we wanted to be clear that the Apple TV+ subscription service for Apple TV content, is not available on iTunes the app for Windows. In order to access this Apple TV+ subscription on a PC, you'd want to use the following options: How to watch Apple TV+, MLS Season Pass, and more
Meaning, you'd need to access this subscription using a browser.
Learn more about Apple TV+ subscription here: Get Apple TV+
For downloading past movies and TV shows purchased from iTunes, you'd need to use the iTunes app for Windows. Which may be why you've been able to download past purchases, but not access the Apple TV+ service through the iTunes app. See the following to learn more about downloading your past purchases through iTunes: Download previous iTunes purchases on PC
If you still need support, please contact Apple Support directly: Get Support
We hope this helps out!
Take care.