A good idea is to get the nomenclature straight. A dry mount is when the piece is completely mounted in a heat press and T hinging is just that.. T hinging. Two separate processes.
As for cutting the mat... you REALLY need to get a better system than whatever you paid $30 for!! It sounds like a pure disaster. Go on eBay and you can find mat cutters for around $100. Try to find one that the cutter head rides on a rod so it doesn't move all over the place and you won't need another person to hold stuff for you.
You may think you are getting by on the cheap with what you have but you need to figure the hassle factor into the project. For what it takes for the 2 of you to get a poorly cut mat, you can do clean, professional looking mats all by your self and repeatedly as well. Spend a few hundred on a better cutter and it will pay for itself many times over in time saved not to mention a better looking finished product.
As for figuring the opening, you now know that isn't the way, is it.
Measure the image and make the opening 1/4" less in each direction. That allows 1/8" overlay of the mat opening. 16x20 image needs a 15 3/4" x 19 3/4" opening.
Another problem with mat cutting is that the opening is parallel to the edge of the mat. If the mat isn't square, the opening won't be, either. Personally, I sort of cheat.. I have a computerized mat cutter. It doesn't matter what shape the mat board is, it always cuts true right angles. Doubt $25K mat cutter is in your immediate future, eh?
Remember, everyone started out sort of like you did....well some did. I went right to a C&H professional mat cutter for about $600 because that is what I was taught on.
Wait till you try to make a frame using one of those wooden miter boxes and a back saw to cut the frame corners!!!
