Neck Pain on Road Bike
If you don’t have any medical neck issues this is probably related to your position on the bike. Before you try any drastic measures I’d suggest playing around with the seating position. First of all make sure your saddle is in a good position. You should be able to ride with your hands hovering over the handlebars. Raising the handlebars is probably possible and should help too.

Maybe because of your braking problems you are constantly looking forward and never relaxing your neck? Try to look down from time to time and change hand positions on the handlebars (that’s what road handlebars are great for!). Braking power could probably be greatly increased with new, good pads and cables.

I’ve noticed that keeping my neck muscles warm helps too. It can also take some time to get used to it. Try to keep the first rides short and relaxed, take short walking breaks, especially before/after longer descents.