Moving the shifters to the down tube is probably the easiest thing to do. My husband likes down tube shifters; I have never gotten the hang of them. The reason nobody suggested that, probably, is that both down tube shifters and stem shifters (what you have now) are something you mostly only see on older bikes.

Before you do it, I would test to make sure you're going to be able to reach them easily while you're riding. If you can grab a water bottle you can use down tube shifters, though.