Hi there!
You could try BZYQT to see what happens. If there was a mild UTI after all (suggested by the antibiotic response), it makes sense to try it.
The other thing I was thinking, was to try adding some Dang Gui to the SMS. SMS is very drying, so if the prolonged Damp Heat had created some Blood deficiency, the alopecia will never fully resolve until a bit of Blood tonification is added. Dang Gui has the additional advantage of being a source of phytoestrogens, so can help hormonally responsive urinary incontinence (HRUI). If the dog is leaking in it's sleep, it suggests the Dang Gui could help there. Note, however, that because Dang Gui is moistening, if we are wrong, it could temporarily send the skin the wrong way (until you discontinued it).
One way to test the phytoestrogen theory, without giving herbs that could send the skin in potentially the wrong direction, is to try the dog for a week or two on soy isoflavones. If you gave a big dose of those BID for a couple of weeks, along with perhaps some calcium, and the dog's leaking reduced, it would support one or both of the above as a strategy. Probably the BZYQT is the least likely to be irritating to the skin as it has less Dang Gui in it.
From a Chinese point of view, one way the antibiotics could have helped is by descending Yang. In Chinese medicine, bitter descends Yang to where it can engage with Kidney Yin to generate Kidney Qi and improve continence. HRUI formulas like Sang Piao Xiao San achieve this using salty herbs instead of bitter ones. If you use a calcium supplement at the same time as the isoflavones, you achieve the same effect, but again don't threaten any progress you've made with the skin. If this approach above works, it suggests the raw may be too low in calcium for this dog, explaining partly why the incontinence appeared in the first place.
If the isoflavone + calcium experiment improves things even somewhat, then the way is paved to safely try BZYQT or Dang Gui as an additive to your protocol
Steve