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The Health alarms you mentioned are *generally* attributed issues with vsanmgmtd on the impacted host - that being said, if there are severe enough issues with vsanmgmtd then placing the node into MM may not be possible which in your case it was and thus other factors (like network in general) should also be looked at.
Where are you seeing the network latency spike - on the vmk used for Management or the vmk used for vSAN traffic?
Regardless, you should be looking at this in more depth (validate end-to-end MTU is correct, using supported driver+firmware on the NICs, no indication of physical issues such as CRC errors/dropped packets or general contention under load).
In general you should (almost always) start with looking at vmkernel.log and vobd.log from times when the issue is occurring, in this case I would also advise looking at vsanmgmtd.log and the output of nicinfo.sh (/usr/lib/vmware/vm-support/bin/nicinfo.sh).
I would advise updating to 6.7 U3 regardless as we have made a lot of improvements and fixes between the build you are on and 6.7 U3/P01.