I don’t think you need a VPN here since you’re using an already secure protocol. Sounds like you’re mostly wanting a static IP address. You can configure the local router to hand out static IPs. Local DNS works too.

Cloudflare supports NS records, which is what you’re looking for. Except it probably only lets you create a zone for the top level domain, so you can only delegate to other providers. AWS Route53 will let you create subdomain zones, and will let you create NS records to set up delegation.

People mentioned Quad9, Cloudflare, Mullvad, and NextDNS already. Controld.com is also available for free with different levels of blocking. They also support DoH and DoT.