Sounds like firewall fuckery. Something doing too much DPI on some interesting looking packets that can’t cope with the volume, choking and dropping what it can’t handle. Check packet loss while this is happening and look real close at the Fortigates. Could also be MTU fun with IPsec in the mix.
Blocking ICMP entirely is a recipe for weird stuff happening. There’s some ICMP worth blocking - redirects, etc - but turning it off entirely A) makes debugging stuff a nightmare and B) can break some things entirely e.g. MTU probing.