" Instead of distributing the fund wholly every 28 days, could we do more limited releases every 7 days?"
The only reason I can see not to do this is to keep the process more simple (which you noted yourself towards the end of your comment.)
In other words, this sounds like a great idea to me. Perhaps projects could simply be submitted on a rolling 28-day payout basis, leading to an over-time averaging out across the whole calendar month.