complicated DNS interception stuff with your router.

It's often not that hard. Many routers have a setting for local dns records.

If you do make a public DNS record, I recommend not putting "plex" or "jellyfin" or "TV" in the domain or subdomain. Make it something more generic.

I recently got a domain from Namecheap, $100 for ten years. If you want something that changes every year, you can get some .xyz domain for like $2 for the first year (and then it'll go up to more the next years.)