I wouldn’t worry about this anymore. This was a big problem during the first few weeks of Apple Music, but they fixed it.
I signed up for Apple Music on day 1, and there was a major bug that could change the metadata on your locally stored music. My library got completely messed up and I’m still finding mislabeled songs 6 years later. I didn’t have a current backup at the time. Just make sure you have a backup, but I wouldn’t worry.
When you sign up for Apple Music on your computer, it will attempt to match your current songs to the songs in Apple Music, and upload the rest. There is still no force upload option.