Try your embassy! You can get married there without your wife being present. Then take all the documents to the local Amphur office and you can get a Thai marriage certificate the same day! But you may need to make a donation to the local orphanage.
So what happens when you have this visa and go back to your own country for a holiday, obtaining an re-entry permit before you leave so the visa is still in force when you return. Will you need insurance when you arrive back?
If you make a donation of at least 500 bht to one of the charities promoted at the amphur office - you will probably find things will speed up considerably.