Wanted to reply to my own thread to thank @RedCruzr_Sprint among others who messaged me separately and helped me resolve this. The answer to the original question, in case anyone else is wondering, is that it's totally possible to sign up for the one-year free with a separate phone and phone number, you just gotta do it with a rep (in store or over the phone) as the online form isn't set up for it.
I wanted to note that in spite of Sprint claiming you can swap devices yourself online, you can't, at least not if your swap entails taking your SIM out of one phone and putting it in another. You gotta ask the chat. This is because the swap self-service tool asks for your new device's IMEI, which is fine, but then it asks for your SIM card's number. And then it tells you it's invalid. Why? Because that number is associated with a SIM in your other phone. It's like a snake swallowing its own tail.
Guys, I'm sorry to do this to you, but I'll probably be messaging you again if SprintCare doesn't help me solve my current problem, which I've just brought up to them. That's the -118 dbm I'm getting on my third-floor outdoor balcony at home. Can't keep the phone after all the sturm and drang if I can't make calls with the service. Fingers crossed. And yes, my area shows "4G LTE Fair Signal" for at least a 40-mile radius, and I've refreshed the profiles so many times the buttons are wearing out.
Thank you for your praise. We're happy to see that everything worked out with the phone and the number. We appreciate the accepted solutions and kudos.
I agree, I hate to have gone through all of that and now the service isn't there for the area. Please do some testing to see if the signal is better once you move away from the building. I understand that you're only on the 4th floor, but we may need to see what height the tower is at.