My interpretation of the pulse getting stronger with tonification of GB 34 is that you are effectively bottling up the patient's Yang, creating more stasis, which is reflected in a stronger pulse. We want a supple pulse, not a strong one. Although you can't be sure until you try, I suspect that sedation of GB 34 would have improved the pulse, and that Shao Yang disharmony is the cause of the dog's stasis.
Essentially, the Shao Yang is like a layer of shrink wrap between the interior and exterior. When You tonify it, it constricts more tightly. In orthopedic cases, we often want the opposite - a slackening of that wrap, such that Yang can escape, pushing Blood before it, into the body periphery and joints.
Even from a conventional perspective, chronic inflammation and degenerative joint disease are blood deprivation states, where there is way too little blood flow, and of a very poor quality, to be able to 'actively resolve' chronic inflammation and provide tissue nourishment. The dog improving as it moves and worsening as it rests (during which blood pools internally) is a clear indication that improved joint circulation is needed to improve joint function.
Based on that, then, NSAIDs should be used only as absolutely necessary to control pain, since the have the opposite effect on joint circulation. Formulas like Xiao Chai Hu Tang and Xiao Huo Luo Dan activate the active resolution of inflammation, gradually reducing pain and improving joint flexibility and suppleness. I would use them both together in this case. XCHT opens the shrink wrap such that Blood can move more effectively peripherally. XHLD is an analgesic and Blood mover (to the periphery). When using Nat Path versions, XHLD promotes (along with Bupleurum in XCHT) the reversal of endothelial dysfunction and the active resolution of inflammation.
Hopefully you see some benefits. I would continue using chiropractic and acupuncture while you use herbs, to confirm their benefit over the coming weeks, as well as to promote circulation in their own right. Chiropractic also helps ensure pain is increasingly isolated just to the joints, and that surrounding musculature is as strong as possible in stabilizing them and restoring the dog to function. Other rehab techniques can be useful here as well, as long as their effect is to promote peripheral circulation. Do not use protocols for treating acute inflammation unless the dog somehow worsens from the above, as it will set back the restoration of circulation. Even then, just use them temporarily, before relying again on herbs, acupuncture and chiropractic
Hopefully that helps you out!