In my experience, a one or two inch difference in pan size has never made any difference.
Of course how LONG and how HOT you bake your brownies depends on entirely how you LIKE your brownies.
I like mine just gooey, with the edges hard and dry.....so I get my soft, gooey brownie and the edges are a nice hard, chocolaty crust. Mmmmmmm
Some people like SUPER gooey brownies, where they kind of ooze a bit when cut. Other people like cake-style brownies, fully baked.
From what you explained, I think maybe your oven is a bit on the "hot" side, so it bakes faster than it should.
You might try lowering the temp just a smidge and see if that helps. Checking your brownies off and on like that shouldn't make a difference either. Now if that were a cake, yes....it could damage the cake and it could turn out flat and tough. But brownies are a whole different beasty.