The OP is in Wales, in the UK. Pricing can be different here so US prices aren't very useful. There also seem to be much fewer vets who have any experience with exotic birds. The competent avian vets *are* often some distance away.
Getting to the root of a neurological issue can be very involved and very expensive, especially if you need to do any soft tissue imaging e.g. through an MRI or CAT scan. However, blood tests should be in the region of £400 - that's what I paid in Brighton. Obviously this differs by practice.
What bothers me about the vet in Rhyl is that he immediately quoted you thousands of pounds without even seeing your parrot and, more worryingly, he didn't say anything about consulting with avian specialists or doing an initial examination then referring you to a more experienced vet.
If you want to try finding a more experienced vet, this is what to look for. The highest qualification in the UK is the RCVS Recognised Specialist in Zoo and Wildlife Medicine. There is also the RCVS Certificate in Advanced Veterinary Practice (Zoological Medicine) - this is sometimes abbreviated as CertAVP (Zoological Medicine). Both of these are postgraduate qualifications, meaning that the vet has graduated from a degree programme, is currently practicing and is doing these qualifications as part of their continuing professional development.
You can click on "Zoo and Wildlife Medicine" in this list:
List of RCVS Specialists - Find A Vet - this gives you a list of Recognised Specialists. As I said, this is the highest level of qualification and not many people have it.
The list of Advanced Practitioners is here:
43 Veterinary Surgeons found who are Advanced Practitioners in Zoological Medicine - Find A Vet
You want to find a vet who is either in private clinical practice or, perhaps, working in a university. Some of these specialists are attached to a zoo and are not available to see private patients.
Given where you are, it may be worth contacting Liverpool University's Small Animal Teaching Hospital to see if they have anyone able to see an avian patient. They're a referral-only hospital meaning that you will have to be referred to them by another vet - they can't see you directly. If I recall correctly, Liverpool mostly focuses on surgery, orthopedics, soft tissue and internal medicine on mammals, but might be worth a shot. If nothing else, they might have a better idea of avian vets in the area. Some avian specialists work from quite small practices and they don't always advertise their services very well.