Is it possible to have my two AppleIDs tied to different services?
To answer my question, after contacting Apple support--

One cannot have two Apple TV+ promotions going on the same Apple ID, or on two Apple IDs that are part of Family Sharing;
One cannot change the Apple ID that used for the Apple TV+ Promotion.

If you want to change the ID associated with a service, at least when you start via a free offer, you can cancel and re-sign up with the ID you prefer.
In my case, since I've got two offers going, the &quot;best&quot; thing to do to transfer over is to redeem the offer while signed in to Music.app, TV.app, or whatever, on the account one wants associated with the subscription.
So make liberal use of that calendar app.