May used to have traditions involving village fetes and the maypole, so at least one of those should be dedicated to local history and crafts. The other May holiday could be a celebration of gardens and growing things. Botanical gardens, garden centers, forests, allotments etc.

And a green spaces day could work really well too! Keeps it super local and it's a nice time of year so you can usually get outside

I love that as an addition to May Day! Local history, village fete, craft contests and prizes, a May Monarch, a picnic- I'd love if we could firmly say "this is a Thing we do in England isn't it cool"