If you keep this up you'll want to add yourself to the public suffix list:

https://publicsuffix.org/

You should also consider grouping your random hostnames under a dedicated subdomain. e.g. "xxx-xxx-xxx.users.tunnl.gg", that separates out cookies and suchlike.

I run a similar site (https://pico.sh) with public urls and thought the same thing for us. The public suffix has some fuzzy limits on usage size before they will add domains (e.g. on the scale of thousands of active users).

I don’t have tunnl.gg usage numbers but I’m going to guess they are no where near the threshold — we were also rejected.