tricky, because usually at trackdays you're not allowed to time yourself unless you're at a proper "test" day.
v de v in france had some pretty random stuff turn up:
https://vdev.fr/resultats2018/
here, the only slightly random example i can think of is donington gt cup in 2018, they allowed some non-lmp3 guest entries, albeit iirc on different tyres. probably a bit slower than you were thinking of though.
https://www.tsl-timing.com/file/?f=M.../183651lm3.pdf