Hmm, a likely place for Pi-hole to wait would be upstream DNS replies, which would in turn suggest that your upstreams are unresponsive.
But that would just repeatedly wait for 10,000 nanoseconds at a time, and also, you are using a co-located unbound which is responding, so that seems unlikely.
Could you please verify that tv_nsec value really is 10,000,000 as quoted in your original post?
The automatic self-healing you observe may indicate that Pi-hole could be starving on I/Os until they become available again, but I can't find an explicit wait for 10,000,000 nanos (10ms), and the only implicit value seems to be used for NTP purposes.
What are your micro instance's maximum limits on sockets and file descriptors?
Does it expose an RTC, and if so, are you allowed to manipulate it?
Run from your Pi-hole machine, what's the result of:
pihole-FTL --config ntp.ipv4.active
pihole-FTL --config ntp.ipv6.active
pihole-FTL --config ntp.sync.active
Also, please provide a fresh debug token, as your previous has indeed expired.