Busted up back, neck and shoulders here too. At age 61 I'm doing pretty well all things considered, but my neck and shoulders haven't aged well.
If I get another drop bar bike it'll be a more relaxed endurance type geometry, bigger tires -- at least 700x28, preferably larger -- with bar tops at saddle height and drops for only occasional use.
For now I'm still enjoying my road bikes ('89 Ironman, Trek 5900) but even after months of physical therapy and lots of work on my neck, there will always be limitations. Some days 20-30 mile rides are fun, and it quickly becomes work after 40-50 miles when the neck pain kicks in.
While I also enjoy my more relaxed hybrid (currently with albatross swept bars), the advantage to drops are the versatile hand positions. Even without using the drops, there are at least three hand positions -- tops, on the hoods, and somewhere between. Most of us shift around those positions a lot. Really helps over longer rides. You might find yourself enjoying longer rides with a drop bar bike set up to accommodate your body.
An alternative? Consider switching one of your flat bar bikes to swept bars -- albatross, North Roads or similar. These are remarkably comfortable and versatile bars, with almost as many hand positions as drop bars. I enjoy my hybrid much more now than when I had riser and flat bars on it. Several other modifications too -- primarily, I switched from thumb shifters to bar-end shifters. Lots of little fit adjustments. I'm still trying to find the perfect saddle, but otherwise the bike is pleasant to ride up to 40-50 miles in a day, usually relaxed group rides around 12 mph with lots of breaks to rest and socialize. Nice change of pace from my road bikes. More fun, less competition and work.