Well the good news is that it looks like the upstream can be set for DOH. They even use Quad9 in the screenshot of the docs:
One thing I’ll mention that’s not obvious as it requires custom conf: dnscrypt-proxy2 can be set to act as a DOH resolver… & then forward requests on accordingly. If you really wanted to maintain control over DNS I don’t see why you couldn’t run dnscrypt-proxy2 on your DNS server, pointing all clients to it. I’ve not tried such a conf however; it is noted in the confs.
So I can concieve as a custom setup in your case of $client → Beryl AX → dnsmasq → Adguard Home → DOH → your DNS via dnscrypt-proxy2 → $upstream DOH (eg: Quad9).
The trade off would be one extra ‘hop’ to your DNS instead of just directly hitting Quad9 but on the other side you’d have the benefit of knowing your DNS is still under your control even when using AdGuard Home.