OP didn't mention what kind of fitness he's in or the kinds of speeds he's achieving. Just upgrading to a bike with aero wheels and that lets him stretch out and get aero will of course add some speed. I've seen a lot of people improve their TT-speeds significantly by using aero wheels and really optimizing their position on the bike (backs and forearms parallel to ground).

Some people are so bunched up on their bikes that when they get down low, their elbows ends up sticking them in the gut or they have to splay their elbows out so far to not hit their knees that they end up block more wind than sitting upright.