You might measure effort in, (aka hours) but not everyone's effort (time) is equal. You might measure value-add, but then nobody wants to do the hard trivial stuff (like docs.)
If it was me I'd likely just have 2 levels, "core" and "casual". With a relatively low barrier to being "core". All cores get the same, all casuals get the same.
Once you stray from "we all matter the same " you invite comparisons etc that will ultimately divide, not foster community.
If you raised enough to have people go full-time I'd add that as a layer above core.
Good luck, and well done on getting the funding.
Unfortunately it wouldn't be easy to actually calculate. The inputs to the formula are "how much of a donation would we have received counterfactually if the team had only included this subset of contributors" for all possible subsets of contributors. Though if it's a small number of contributors then you only have a 2^(small number) of counterfactuals to pull out of nowhere.
then normalize so all the users add up to 1, use that as your coefficient on disbursements.
Of course it's gameable, hopefully there's a BDFL to guard against test/commit stuffing or other bad faith things.