Fantastic idea. One possible way to implement it would be this:
A randomised draw amongst the entrants. Would have to have some sort of control to ensure not duplicate or fake accounts.
The winner posts 10 new steemit posts, and everyone who wants to contribute to the winner can go down and upvote all 10 (or a few). Or just send them Steem.
Another idea would be to delegate steem power to one user for the period, then after the next draw all tje delegated power could swap to the new person.
Thats a very smart way to steemify the entire thing, good idea!
If I have tons of steem power, and host a draw, will that help me generate more steem to give to the winner? (still learning here)
You could send the SBD direct to the winner and save the steem power for delegation/ growing the account.