I think the XCHT is a great idea, given the:
- Seasons of onset and aggravation (spring and fall)
- Concomitant Stomach Yin deficiency, evidenced by GI ulceration and the time of vomiting (when Yang Ming or Stomach dryness) is peaking
- Improvement with NSAIDs, which implies a Stasis condition of some type
The Stomach Yin deficiency is often tied to Blood deficiency in general. Bu Gan Tang won't particularly address the Stomach, but has Blood tonics that help resolve any associated spasm. Yi Guan Jian will resolve the Stomach issues, but doesn't have the antispasmodics. For me, then, I would try Yi Guan Jian and add in Mu Gua (maybe 15g per 100g) to have the best of all worlds, but if right now all you have is Bu Gan Tang on your shelf, at least start with that. Continue the XCHT at the same time.
Chiropractic is usually needed in these cases to provide rapid relief. Do you have a local resource you can send her to (if you don't do it yourself?). Otherwise, gentle manual mobilizing of the entire neck is called for, from the atlas on down. Basically you are trying to rock the vertebra, pressing down on the transverse processes and pillars, first on one side, then on the other. When you find one that doesn't dip on one side as much as it does on the other, it needs to be more firmly nudged downwards as you're manually mobilizing things.
As for pain killers, gabapentin may be a better choice for this dog, since the problem is most likely nerve root impingement, given the involvement of the neck, forelimbs, and (apparently) the Shao Yang. Maybe see if that drug gives the dog more relief, at which point you can start finding the lowest required dose of the NSAID, thus giving the stomach a break. The Blood and Yin tonic is still needed, though, even if the vomiting stops from the change in drugs.
If you're seeing limb atrophy, then there may be a peripheral nerve lesion. Rule outs would have to include a tumor. But if 'weaker' doesn't mean 'atrophied', then the above approach is the first thing I would try
Hope that helps!