A technique I have a lot of success with is asking why <some observation> doesn't change their opinion. It leaves the doctor in a position of expertise and authority, so they're usually happy to spend the time teaching you. Normally I learn a lot about some gap in my medical knowledge, and sometimes the additional reflection changes the doctor's opinion and gives me better outcomes.
Depends on if their mind is made up. Yeah, I failed the food challenge test because you used the wrong thing! No, you can't use pork in place of ham--the trigger was something that gets added in the process of making it ham.
Kind of. Even when their mind is made up, they're likely to try to answer (since the framing places them on a pedestal). Both you and the doctor will notice anything obviously wrong with the answer. I've met a few young doctors who would dig in their heels (different from explaining why they're right; if they're actually right and teach me why then I think that was an incredibly valuable opportunity), but you ought to, in most parts of the world, be able to fire them and find somebody actually willing to talk to you. Almost all of the time I meet doctors who handle the framework I set out exceptionally.
Your pork/ham comment is interesting. For other toxins/allergens/..., I see doctors very explicitly examining every possible extra ingredient/factor before even deigning to consider that the bulk solid might matter (e.g., most chocolate allergies are actually to soy lecithin or one of the other mixins). I'm surprised anyone would rule out a ham problem just because they tested one kind of pork.
It's obvious he thought the problem was upstairs. If you're a medical mystery they're going to consider psych and some of them will consider it too much.