I've recently built something similar [0], but the complete opposite. I wanted to forward traffic onto my homeserver without a public IPv4. I've tried Tailscale Funnel, but the inability to use custom domains made me look for other solutions. I ended up with a fly.io app acting as a TCP proxy over Tailscale. Considering how crappy the setup is, it's surprisingly reliable. Great job fly.io and Tailscale teams! I haven't had any issues in the month or so I've been using it.
I've launched Wireshark monitoring DNS traffic of roughly 5 phones. I've collected 19.8k DNS packets so far. Out of that, 5.1k packets are flagged with REFUSED or SERVFAIL. If I am not mistaken, it means that 51% of DNS requests fail.
Looking at queries for graph.instagram.com, it looks like there are roughly 20 attempts in a sequence before it gives up.
All in all, this could probably explain doubling of the DNS traffic. But the sample is rather small, so take it with a grain of salt.