For anyone who comes across this in the future, I was unable to get a class 1 medical about twenty years ago due to colour vision deficiency (mild protanomaly), but (in the UK) over the summer I sat the “CAD test” near Heathrow with these people https://www.aviationvisionservices.com/about-us/ (cost £120 approximately) and was able to have all restrictions related to colour vision removed from my medical, including the option to get a class 1.
At least for a UK CAA licence, this is a single test, valid for life.