I too have DNS issues with meraki.
From my testing it is related to the option "use upstream DNS",
ISP DNS = pages load instantly
google or any other dns = pages load instantly.
Use upstream which broadcasts the gateway ip as the dns server and then sends the traffic upstreme to the ISP,s dns is where the issue lies.
If you are fortunate enough to not have any configs that are sec dependent on DNS, just change the dropdown on DHCP dns settings from Upstream to anything else. you can manually enter in one or I just selected use Googles Public
Problem solved.
But the actual problem is not really solved, there is still an issue with Meraki, case has been escalated.
Hope this helps
R
Dan