If money is no object, one of the major schools like Oxford has the fleet size and experienced instructor force to give you gold-star training
So you might think, but Oxford do not offer FIC courses to the general public, a large FTO is more concerned with training airline pilots than instructors. Large schools usually have the facilities, so that they can train and standardize their own FIs.
Larger more commercially orientated schools tend to have a conveyor belt mentality
I am not aware of any FTO offering FIC that has anything like a conveyor belt mentality. It takes 5-6 weeks minimum to train a FI, it is hard work, one to one, and most FIC instructors are self employed because FTOs cannot afford to employ them; consequently FIC training is a cottage industry lodged within larger organisations.
There are two distinct styles of FIC, one based upon CFS teaching from the 1950s and a smaller number based upon more recent CFS teaching.
An FI may find a particular course to their personal liking but it will be some time before they can actually judge it in a truly objective manner. As you only ever complete one course, you will never have anything to compare it with!
Quite often schools prefer instructors who have been trained by people they know, so it might be a good idea to look at possible locations you could instruct at, and then see if they have any recommendations or, more importantly anywhere they would not accept!