Setting up NextDNS on TP-Link ER7206 fails

I am trying to set up NextDNS on my TP-Link ER7206 router (school environment). It normally uses Google DNS, which works flawlessly. But when I change the (WAN) DNS settings to NextDNS' IP addresses, all DNS requests fail after a few moments. (It seems like it works for a minute, and then goes down.) Then, I am even unable to do nslookup specifying the NextDNS servers (request timed out), or setting the DNS settings manually in my network card configuration.

-> If I do this BEFORE the router changes to NextDNS, everything works fine (but just one client of course).

After it has gone down, I have to give it 10-15 mins to 'recover' before I can use NextDNS again on my computer.

I also tried:
* setting NextDNS servers in the DHCP section, so pushing NextDNS to the clients, bypassing the router itself
* setting 'DNS Proxy' on the router, so rewriting all DNS requests to NextDNS DoH

But all with the same result. I am currently unable to figure out if the problem is in my router, or in NextDNS itself. Could it be that NextDNS goes down when it receives many requests coming from the same IP address? (School environment with 250 clients.)

I am currently using the free plan for testing purposes. I want to be sure everything works before we pay a subscription.