I don't know whether or not you remember, but a couple years back, BigBlue came up with this idea of a format called "Top Deck" where each player starts with no hand and can choose any card in the game each turn to put into their hand. I played a few games with BB and it was a lot of fun, but insanely degenerate and time-consuming, so I was thinking of tweaking the format a bit to dull down both of those problems. I had two possibilities in mind (which, looking back, were actually suggested at the time):
Top Deck Limited: We start out with a pile of boosters. Maybe 6 to 10 total. All of the boosters get opened and revealed. We do a mini-draft of 2 to 6 cards each, which will be our opening hands. After that, each player takes his turn, but instead of drawing you pick a new card from the pool of cards that were in the boosters (or a basic land.)
Top Deck Constructed: We each pick 40 to 60 cards from an existing format (Standard, Modern, pick-a-Block, something else that isn't Legacy or Vintage or Classic or whatever Type I is called nowadays). All those cards get pooled together. Play proceeds as per standard Top Deck rules.
Original Top Deck Thread
Some general rule alterations that apply to either choice:
-No need for a best-of-five series
-No maximum hand size or card draw limits
-Shared library instead of individual ones
-Cards can go back into the shared library instead of always getting exiled