What are your goals in cycling? Do you race? How important is it to go a little bit faster? How many more years, or decades, do you want to continue riding?

I ask these questions because it seems to me that in addition to not wanting to listen to the doctor, you're not listening to your body. Rather than changing the type of bike you ride, you could modify your roadbike. I found that the more hours I rode the more my neck would hurt because of bending up to look forward when by body was leaning forward. I replaced the handlebars (and necessarily the shifters and brake levers) with straight across handlebars - still weren't high enough, so I got an extension to lift them even higher. I can now ride sitting up, bend when I want to. The bike is still pretty light, but unquestionably the aerodynamics are not good and not as fast as the bent-over position. So goals are important - for me the goal is not speed but to enjoy the ride - for years to come.