My site offers appointment scheduling, my customers like to put our site inside an iframe on their site so their users don't get sent off to a domain they don't

My site offers appointment scheduling, my customers like to put our site inside an iframe on their site so their users don't get sent off to a domain they don't know. Our site needs cookies for sessions, no tracking is involved, I would say that's a perfectly legitimate use of third party cookies. I just tried the new Safari Preview and this indeed stopped our framed web app from working. I managed to get it somewhat working again by asking permission via the new Storage Access API. Yet another popup users need to click through, ugh. I also managed to get one Safari Preview in a state where it would consistently deny access, without prompting the user again. This is going to make for painful support tickets. I guess a more permanent solution would to ask my customers to put a piece of JavaScript on their page so we can set first party cookies but that seems a support nightmare as well. Any other suggestions to work around this would be most welcome.