For what it's worth, another data point or two...
My wrists, elbows and shoulders demand drop handlebars, and I went with Thorn's Zoom 44cm (c-c top and bottom) anatomic-bend drop 'bars on my Sherpa, since they are right at the width of my shoulders, and I wanted a bit more leverage with a full set of front panniers and HB bag on rough tracks and off-road. I use Nitto B115 handlebars to captain my tandem, which measure 45cm c-c at the ends and 42cm at the tops of the brake hoods. These are both much wider than the tops of the Nitto Randonneur handlebars used on my other single bikes, which measure 45cm c-c at the ends but only 37cm c-c at the tops of the brake hoods. I mount my brake levers fairly high and the randonneur-bend has very shallow reach and drop, so there is plenty of incentive to actually use the drops, say in a headwind. Perhaps a switch to 'bars with flared drops (like the Nittos) would give you the best of both worlds -- narrower for cruising and neck comfort, but wide for stability when you hit the drops. When I ride the brake hoods on the Nittos, my elbows are splayed to the sides a bit as well, but inline when on the drops. The flare keeps me from hitting my wrists on the return above the "hooks". I always ride with elbows bent a bit anyway to provide some shock absorption.
Another thing I decided to add to the new Sherpa was a set of Tektro RL740 v-brake compatible "interrupter" brake levers, next to the stem at the 'bar tops. Designed originally for the cyclo-cross market, they are a really nice option for when one wants a complete change of hand position with ready access to the brakes. It might be possible to fit shimmed interrupter levers to even straight/comfort handlebars for a secondary position. I have seen a pair mounted on tubular bar-end extensions with straight 'bars. A person could always go with Origin8 bar-end adapters and move them in progressively till the neck pain eased.
If the steerer remains uncut and fully shimmed, it might be possible to mount a secondary handlebar on a second threadless stem to see if that helps. It would certainly make it easy to switch between one and the other. The late Sheldon Brown did something like this using a quill stem to mount the secondary handlebar on his Thorn Raven. Pictures of the setup are here:
http://sheldonbrown.org/thorn/ In my book, whatever works to get and keep one riding pain-free is worth a try.
You might also try altering the reach with a stem that varies in reach and/or rise while keeping everything else the same. That would be something to try for minimal cost and effort, and an understanding shop might even loan a stem if it is the threadless type with a top-cap for ease if fitting.
I prefer the tops of my drop handlebars to be equal in height to the top of my Brooks saddles, but that is only a personal preference that has worked well for me in well over 200,000 miles. Everyone is an individual, and some people are far more comfortable either more upright or um, "declined" a bit more. Certainly, racing bikes always look more "race-like" in the brochures with the saddles well above the 'bars, and many buyers seem happy with them that way. Some of the Dutch riders I saw on their city bikes nearly leaned backward they were so upright, and they too were happy. I seem to have found joy somewhere in-between. The point is, handlebar height as well as width and reach can make a difference in overall comfort and it is a factor in neck pain. My father broke his neck in a car accident as a young man, and suffered neck pain while riding if the handlebars were even a few millimeters above or below his preferred height. Same for reach and width.
Neck pain while riding can be down to so many subsidiary factors besides the obvious. By any chance, can you borrow another helmet (If you wear one) to see if that is a contributor? Sometimes weight, shape, or the helmet harness and closure can all make a difference depending on how upright one's head is held while riding.
Best,
Dan.
