The core of this problem is I really want to avoid using the Music Manager ever, at all. It's already wreaked so much havok on my local music collection that I'm not sure it's worth the trouble of finding and deleting all the duplicate download files and fixing all the metadata again, so I'm just giving up and going to use their cloud service exclusively. (Was that their plan all along?)
I do plan to do most of my purchasing from Google Play in the future so as to avoid the necessity of transferring stuff from Amazon, but I'm gonna get Amazon gift cards a lot more often than I'm gonna get Google gift cards, so…
Best Answer
As with transfers between almost any two competing applications, transferring music from Amazon Music to Google Play Music is not as simple as clicking a couple buttons. You are unfortunately going to need to download from Amazon and then upload to Google.
However, you do not have to use Music Manager to upload music to Google Play. While, in my own experience, uploading using Music Manager tends to be quite a bit faster (when it works like it's supposed to), if you have Google Chrome and have also installed the Google Play Music for Chrome app, you can open up Play Music in Chrome and simply drag your downloaded Amazon music files from your file browser and drop them into the Play Music tab; this commences the uploading process, which uses Chrome itself rather than a dedicated client like Music Manager, for whatever you dropped in.
For more information on uploading using Chrome and its official Play Music app, check out this Google Play Help Center article.