Hair matting

I have a 29 pound Maine coone cross who is very terrified of everything like loud noises and he is not very  social in the being able to pick him up and hold him department. He freaks out when we try and put him in a carrier for vet visit and cannot be groomed. Because of his size he sometimes gets mats under his front arms and chest area and he doesn’t like to be brushed long enough for me to work them out. He bolts when I bring out clippers and he gets away if I sneak scissors near him and try and clip them out. The vet gave some gaba pills but they are huge and he won’t take them. Any help to get him calm?