I only know of the vets recommended on the Aus. rabbit vet site, and his name isn't mentioned. Maybe Azerane would know. But it does seem like your options are limited. You could always get a second opinion from one of the other rabbit vets on the list or have the vet consult with a UK specialist, especially before any surgery is attempted. Though I'm not quite sure why they are even suggesting surgery at this point, if that is indeed what they are doing, especially if it is an infection that they suspect and regular antibiotics haven't even been given a good try. Do you know exactly what it is the vet wants to do or is thinking in regards to what they have found so far?
If you are unsure of the vets rabbit experience, I would certainly want a consultation with someone that is a confirmed rabbit specialist, before proceeding with any type of surgical procedure. Case in point, another rabbit owner in the UK took her rabbit to the local vet due to GI stasis symptoms. The vet was recommending abdominal surgery. Abdominal surgery is usually 50/50 on whether the rabbit survives. She thankfully went for a second opinion to the rabbit specialist FHB, who did not recommend abdominal surgery and found the stasis occurred due to a sliver stuck in the rabbits tongue. Procedure to remove the sliver and the rabbit is fine. A rabbit savvy vet can make all the difference in correct diagnosis and treatment. My suggestion, consult with a specialist in the UK if you are unsure of the rabbit savviness of your vets and the treatment, and don't have a known specialist there, especially if they are suggesting surgery. Because there are so few good rabbit vets out there, we have to almost know what is really needed for our buns and be their advocate in making sure the right thing is done.
I'm also not sure that you want to be putting your rabbit through any additional stress at this time until you have this GI stasis situation sorted and she is back to eating well and her usual self. She'll be in a weakened state due to this and that's not usually a good time to be complicating things with surgery or other procedures. The only way you want to go forward with further treatment is if her underlying health issue is contributing to the stasis continuing and not clearing up.
Is your rabbit on pain medication, and if so which one(s), the dose, concentration of solution, and how often? Inadequate pain medication could be one explanation of why she is doing better at one part of the day and worse later on. It could also just be the stasis, as it can be a bit or a roller coaster as they are recovering.
