There may be a problem with your setup(?), as it would be quite a problem, if the known (trusted) DNS servers did not respond to the ping and would the provider's CPE restrict you from using ping ???
(this is just an idea why you can stop pinging from a known DNS server, for example, make sure the gateway IP, DNS severs, WAN IP, etc. are in your HOME_NET list / IPS/IDS)
We have been using Cloudflare DNS servers (1.1.1.1 / 1.0.0.1) for many - many years for monitor IP purposes, we have never experienced the problem you outlined.
Many ISP gateways really do not respond to ping, so a known DNS server is a good solution.
Test the best DNS server for you, starting with:
https://www.grc.com/dns/benchmark.htm
Or use this and try to PING the selected DNS server from a desktop machine for a long time and analyze the values obtained:
https://emcosoftware.com/ping-monitor
I don't think the multiple - gateway monitor IP is the solution, it would only bring more measurement tasks and results to the system, this is irrelevant here.
PS:
We have had the experience that sometimes on a self-made (from internet) blocklist, 1.1.1.1 is added to the list of banned IPs, the list is periodicaly updated on the firewall and 1.1.1.1 no longer works.
What did your own ISP answer this question? (FRITZ!Box vs. PING issue)