I looked at the internals. The difference between desired 1000 TPS and max is that in the later case the Thread.sleep is called (actually if you have more than 0.5 ms to spare). I am guessing that probabilistically Thread.Sleep is called couple times per round.
I do not know what java does when thread is asleep, but I would imagine that the garbage collector and other gizmos kick in during the sleep. While at max TPS the java chooses as it wishes when to run GC and if you are the unlucky one, the GC time will be counted against your bot. This would explain sporadic super long executions in my bot time profiling.