> don't know how much memory my shared hosting allocates,
You can see a general, maybe not 100% accurat number right on the admin overview page among other info. There is also a utility named "php info" that will list the PHP configuration details (using a standard php function for that).
> If the issue turns out to be server response time to render even cached pages, memory wouldn't make a difference, would it?
Well, memory of course generally can have performane input.
> They don't always have a magic answer, but they always respond carefully and thoughtfully.
Of course, that is understandable, they cannot know every tool anyone uses on their server. But they should be able to tell what might cause this delay.