Swapping Between Nexus 4 and iPhone 5 on AT&T: Impossible?

Some background:

I own both an iPhone 5 and a Nexus 4. I have a AT&T for service and have had them for years now. With my latest upgrade cycle, I bought the iPhone 5 through AT&T subsidized and then bought the Nexus 4 through the Play store, obviously. When I got my iPhone 5 I activated it through AT&T, which provisioned my data plan for LTE service. Eventually I misplaced the 5 for a while and put the sim in my N4. I had to call and "activate" that phone since it didn't pull down data initially. Per my understanding, AT&T proceeded to change my data plan to 3G only - when I went to use my iPhone 5 again, it could not get LTE.

My dilemma: I want to be able to switch between my iPhone 5 (and get LTE!) and my Nexus 4 at will.

After speaking with a rep from AT&T for some time, this is apparently impossible. The best I can hope for, she said, is getting 3G on both phones. If I want LTE, I'm locked to just the iPhone - the LTE plan will not work on the Nexus 4. Here I turn to you, Verge faithful: Why is this? My iPhone 5 will still get 3G/HSPA+ speeds if it cannot get LTE (I know this because we only recently got LTE coverage). So why can't my Nexus 4 get that same data? Is AT&T stopping me somehow? Last summer, I was in a similar situation to this one, except with an HTC One X (LTE) and iPhone 4S (3G/HSPA+). It was a bitch to get working, but somehow I could get both LTE on the HOX and 3G on the 4S. Per my discussion with the rep, this was "impossible" and if I got it I was just "lucky."

Has anyone been able to achieve what I'm after? If so, how? I do not understand why I can't still get 3G on my N4 if my plan is "provisioned" for LTE - my iPhone still gets 3G when it can't find LTE - the same 3G my N4 would get (if I'm not mistaken). Is this a technological limitation, or some draconian fuckery from Ma Bell?