I will live with the dry mounted prints as they look better to me. If I do the other mounts it is usually with smaller prints that won't be in the frames very long. Either way, test the product before mounting an important print. Make your mistakes with work prints rather than your exhibition work. Then, when you are confident in the heat setting with your dry mount press, for that you can make nice t-style hinge mounts, do one with the important artwork.
Mats are a problem for many photographers.
Just as it took time to learn how to produce good images, it will take time to learn how to mount and then cut mat board. Small edge overcuts. Ragged and crooked cuts. Mis measuring and miscutting both happen. It takes time and it takes patience.