My son is the same age as yours and I had the same problem a few months ago. I was already using 2 liners but it wasn't enough. Someone on the Forum suggested putting the third liner outside the diaper to minimize the bulk. I tried that and it worked like a charm. I fold the liner and place it at the front, where it gets more wet, on top of the diaper. It's held in place by the cover. You may want to try.
As for the potty, it has helped us, too. We got a cheap and small one from Ikea, my son loves using it since we babysat a neighbor who was potty-trained and he saw her using it. He doesn't always pee when he sits on it, but he often does. I figure that's a good start! And since we started doing that, the diaper is a lot less soaked even when I forget to put the extra liner.