Wow, what a horrible time she has had...so is she having surgery to remove the embolism? Where is she on that situation? Because one may influence the other...
Honestly, in my own personal opinion if it was one of my babies, and also in my medical opinion, I would just get that tail amputated about a half inch or so above the line of necrotic tissue. I would not at all mess around with any more antibiotics for sure, she will be on more antibiotics if she has surgery to remove the embolism for sure, and honestly in a completely healthy dragon with either an infection in their tail that is causing spreading necrosis (Tail Rot) or once with a circulation issue causing necrosis, antibiotics typically do little to help stop it, nor do topical treatments like prescription antibiotic cremes, Colloidal Silver, etc.
The circulation to their tails is poor to begin with, which is why infections in their tails is so hard to treat with antibiotics, whether injected, taken orally, put on directly in a topical form, or all 3. It rarely works to stop the spread of the necrosis. As I recall the issues with her tail started quite a while ago, from the end/tip of her tail, correct? It could have originally been caused by a localized infection, a tiny band of retained shed that was constricting the blood flow, it could have been the embolism in her abdomen causing a constriction in the blood flow to her tail (you don't know how long that embolism has been there growing, as it wouldn't show up on just a plain-film x-ray like the follicles would), or the blood flow may have been effected by the generalized swelling caused by the embolism. The tissue of the tail itself does not look like the typical necrosis that is caused by a bacterial or fungal infection that keeps spreading upward and causing necrosis all along it's way towards her body (Tail Rot), typically that tissue outwardly looks "infected" and actually turns black, shrivels up, and then falls up, while the necrosis continues to spread up the tail, which is visible by the black tissue spreading. That's not what the tissue of her tail looks like, it just looks like it's becoming hardened and then drying up, which to me represents a circulation issue to her tail. Any way you slice it though it doesn't really matter what the cause is, it's not going to stop spreading, at least most likely it's not going to stop spreading (especially if you don't know the cause).
If the embolism is the cause of the issue and is what is effecting the circulation to the tail (It would have to be effecting the circulation to her "Ventral Tail Vein, AKA the Coccygeal Tail Vein), which is also the vein they typically take blood from at the base of the tail (I don't know what the timing was regarding when she first had a blood draw done from her tail and when the tail tissue started to show signs of dying), yes if you remove the embolism successfully that would also likely restore the circulation to the remainder of her tail, but the problems with waiting are #1) You don't know if that's the cause to begin with, #2) Even if it is the cause it doesn't mean that restoring the blood flow will stop the necrosis anyway, and #3) If you wait to do an amputation above the necrotic tissue line and there is an infection of some sort, that infection could cause many complications with the embolism, especially AFTER the surgery to remove the embolism. The last thing she would need after an embolectomy would be a remaining infection in her tail spreading to her bloodstream.
She doesn't need her tail, and in my own opinion it's not worth waiting around and trying to do cultures to determine the correct antibiotics to try, then trying different antibiotics that probably won't work, and she's already stopped eating her normal diet, etc. I'd just have the amputation above the necrotic line done ASAP, it's a simple procedure that isn't that invasive at all, and it will stop the issue on the spot.