Flat bar or drops?

[aicabsolut]

I'd say go with a compact drop bar. The advantages of a drop bar, even when you are not using the drops, is that you have more hand positions. It could be that just rotating the direction of your palms can help you find a comfortable spot relative to your neck problems.
Having a shallow drop bar means that when you do get in the drops, you won't notice a significant difference in how much more you have to look up to see enough. Use the drops sparingly, like when you need to do a lot of descending. Then, you don't need to necessarily look way up the road (you are kind of looking down the road anyway), but you will have some of the handling and stability advantages of a drop bar. You can also make drop bars fit you as relaxed as you need. If you have to crane your head up too much for your comfort, then you've gone to aggressive. A Specialized WSD bike will have a shorter reach (shorter TT) and a bit taller of a head tube. The Roubaix would fit you if WSD geometry (in the TT especially) isn't for you, because it is relaxed with a 2cm taller head tube than more aggressive bikes like the Tarmac or Allez. You may need average outward reach, but you don't want to go too low in front. If you like Specialized, I would look at the Roubaix and Ruby or Dolce. FYI, the Ruby has some aggressive bits to the fork rake and rear triangle that the Roubaix does not have (for handling, stiffness, and responsiveness purposes), but for sizing, the Ruby runs approximately one size smaller than the Roubaix (i.e., a 56 Ruby is similar to a 54 Roubaix).

[aicabsolut]

Oh, as for drop bars, you might want to consider the following compact or WSD bars:

3T (i forget which one is which, but they have some very shallow drop bars now, that come down to a 38cm size)
Specialized WSD bars
Bontrager WSD bars

These are probably the most shallow that I've seen lately.