You should always ask a priest.
But in general a JOP wedding is just a legal wedding and not recognized by the Catholic Church. So if you do that you would be sinning because as a Catholic you are required to follow the church requirements for marriage. If you do this you wll need to have your marriage blessed but will also have to go to confession . The Church most likely won’t permit you to have a public second wedding ( but I’m not sure about that) if you willfully go and seek a JOP wedding. So that is why you need a priest.
Why don’t you just get started on your marriage preparations with the church? The Archdiocese of the Military has dealt with this situation before. You can do this prep in two separate locations if necessary.
Joe and Kathleen it is wonderful that you want to seek a lifetime of love , companionship and working together as one for the glory of God. But you need to do it right. The only way to have the full Catholic wedding is to follow the churches guidelines on marriage and to make sure you are in a state of grace at the time of the wedding vows.
Living together is a separate issue. It’s very difficult to do without sinning (physically) and it is a source of scandal which is a sin. The Church does not approve cohabitation . People who cohabitate have a higher divorce record. Don’t live together .I’m confused about living together anyway if you are an ocean apart? Does getting a JOP wedding mean one of you can transfer to be with the other?
How will you feel closer by getting a JOP wedding? You will not be able to consummate that legal agreement without sinning. That will actually separate you more on a spiritual level(husbands and wives marry to lead each other closer to God not farther away and certainly not in sin) as well as separate you from the church.
So, Get Thee To Your Priest(s)