That's your best bet. I was fortunate enough to have "swap for Maxx" noted in my account if I should ever want to switch. I was tempted to try the same deal with the SIII, but that home button really cramps my style. From my experiences, here's what you need:
(1) Longstanding customer. Better part of a decade, no less. I've had a line with Verizon for about 9 years now and my line is the "first" line in the family plan. Each line is added to mine, so I get the uber-awesome status. 9 years ago it was just my line, now it's 5 lines with unlimited data. That shows loyalty and they love that.
(2) Polite. Don't yell; this is obvious, but some get upset really quickly hiding behind a phone.
(3) Don't out and out ask, but dodge around the issue. "Is there any alternative to me getting another replacement? I just want a 4G device of comparable value and meaning." Stuff like that. If you say, "Yo homey, give me a Maxx" you're dead on arrival.