Hi Corinne,
Your ideas area all great. The first thing to make sure of, though, is that the dog is not in pain. Pain worsens at night and can cause panting and a secondary increase in thirst. A thorough chiropractic evaluation and possible adjustments seem called for. Often after adjustment, massage or manipulation, the pulse is much more palpable, allowing you to test its response to acupuncture. Given the purple tongue, ruling out a Shao Yang disharmony manifesting as pain in the L-S region would be most important. Points that would improve the pulse were that present include BL 28 and GB 34
Some other possibilities also exist. The purple tongue, hard to feel pulse and Dampness all suggest San Ren Tang to me, which can be of use in low back pain if it turns out to be present. Otherwise, a purple tongue, weak pulse and trembling legs suggests Kidney Qi deficiency, calling for Rehmannia Eight. Any suggestion of cardio-pulmonary disorders? If so, then Xue Fu Zhu Yu Tang sounds like it is called for given the tongue and pulse. If you used Modified Xue Fu Zhu Yu Tang, you'd get the benefits of Turmeric on joint inflammation.
Lastly, have you explored how this dog could be so heavy on a homemade diet? Is it high in fat or carbs? If so, that will keep any dog Damp. Otherwise, if it is a lean meat- and vegetable-based diet, you should rule out or address any hypothyroidism.
Sorry to just be asking questions and not giving you a single definitive answer. Hopefully these ideas help you out anyway
Steve