I competed as part of a team (we won :D) in a competitive bioblitz via iNat last year: https://www.inaturalist.org/projects/international-biodiversity-championship-2020
The ‘rules’ were purely most species wins, so that would be one option.
One of my colleagues ran something similar in Australia earlier this year, but approached things differently. They got a list of species known to be in the reserve, and then assigned each one a point value, with rarer stuff worth more, common stuff worth less. They then scored each participant/team based on this system, with extra points awarded for species new to the reserve. Apparently it was quite successful.