I highly doubt anything cloudflare did resulted in that otherwise there would be very big outrage in this discord right now and a lot of unhappy engineers having to work to get that fixed asap
If your origin doesn't work over https at all, it would only have ever worked with Flexible. If the origin does work over https, and responds with an invalid (wrong domain, self-signed, etc), but only full and not full (strict)
There is one quirk with Cloudflare you could potentially take advantage of. If the customer proxies a CNAME record, Cloudflare is fine as long as the certificate it responds with contains the requested hostname, or the target hostname. If you have a record like custom-hostname.yoursite.com, all it has to do is have a valid cert for itself.
In a perfect world though, you should really be using something like Cf for SaaS/a setup that issues a cert for each customer, like every other provider does