After a few rounds of normal combat, the Explorator decides that he would like to pause a second so that the Arch Militant can take his turn before him. He doesn't want to "Delay" because there is no condition he is looking for, he doesn't want to be limited to a half action, and he wants to be after the Arch Militant for the rest of the combat. Can the Explorator voluntarily lower his own initiative value so that he can henceforth go at a later point in the round?

(This would be a Delay in the d20 rules system.)

In terms of the RAW no, there is no such action or option. Simply put the combat is all happening at roughly the same time and delay is the best you can hope for. Essentially the other half of the players action is them getting ready and waiting for the other person to do something before they act and thus they have only the other half left. Your GM may of course always house rule it if they find it a problem.