So how long to you expect to be in the military ?
It is a hard situation, approaching women while already technically married. Is your wife willing to verbally confirm your situation to a potential interest ? This would be critical. Not that it will probably raise your success potential much - but a little can be all that's needed sometimes. But you're wise not to get your hopes up.
If you end your service and get back to the mainland, then you two can have a better discussion about the best course of action going forward. If children are really important to you, legally you will probably need to divorce, as the current laws would not allow benefits from a non-spousal arrangement.
I'd say go explore, see what happens. Nothing ventured, nothing gained.