At this moment the transmit timestamps of the monitoring queries are random values. The explanation is that it is for privacy (sic!) and prevent spoofing. Isn’t the UDP source port for the query is random enough for the same purpose? Or as a compromise, for the transmit timestamp use the local time minus a smaller random value ( 2 bytes long). Together with the UDP source port that would give about 31 bit randomness, which I believe would be sufficient protection against any packet spoofing attempt.
We should exclude the possibility, that certain packet drops are due to some router are checking for crazy transmit timestamps (for example way ahead in the future).