First off, very cool idea. I'm a fintech PM and had the idea to build something similar. Glad to see someone doing it!
From my research, it sounds like, because prize linked savings accounts are so new in the US, it's unclear whether requiring someone to have an account would count as consideration. By offering an AMOE are you taking a conservative position on this until it's more clear? Or, has a judge/court ruled on this?
I was involved in a sweepstakes at a bank a couple years ago and we took a similar route as you, offering a mail in AMOE, requiring handwritten entries. Without any marketing, we received several thousand entries, mostly from people who mail in entries to every sweepstakes they find.