You have my fullest sympathy for yoru SI joints! I ahve problems travelling as well.
As for seeing Prof G, what usually happens is that he will write a report of his findings and then make recommendations for your local service providers to consider (unfortunately, at the moment there is no guarantee that they will follow his recommendations or anyone elses from outside your local service providers).
He may suggest you need physio and refer the physio to the book written by Rosemary keer and Prof G on the 'ecognition and Management of Hypermobility Syndrome for Physios'. He usually refers to thebook directly. He may suggest you see an OT and/or a podiatrist or be referred to a pain management course or pain clinic. Depending on your condition he may suggest seeing an orthotist but things have to be quite serious for that. He will then say whether he needs to review you.
From there on it is up to your local service providers to get their acts together to meet your needs. If they dont meet your needs by the next appt he may suggest a rehab stay there or possibly a referral to another rehab service again that depends on what he finds on examination and during clinical discussion.
I hope it helps. Reports can take up to 8 weeks at the moment due to oversubscription of the HMS clinic.
Abi and I are visiting with UCH and its staff in a few weeks to have a chat about the needs of a HMS patient, not because there is a problem there BUT because they really do want to provide the best possible services and are kind enough to listen.