I don't have a lot of detailed input, but I can tell you your thread title is a chicken-egg sort of thing. Bike fit will affect how you sit on your saddle. What saddle you're using will affect your bike fit.
I guess my #1 suggestion would be when you get your fit done, do it somewhere that lets you come back for tweaks at no additional charge for a certain period of time. Since your saddle works for you when you're upright, I'd start where you are - get your fitting done, see how your saddle works with your new position, try other saddles if you still need to, then if/when you find a better saddle, get your fit tweaked again.
My experience is that depending on the community, unfortunately a lot of bike fitters know very little about saddle fitting. So one thing you might do when you're shopping for your fit is pose the question to them ... if they tell you that your saddle won't affect your fit, or suggest saddles for you without asking you about your specific saddle needs, then go someplace else.
I'd say also that embarrassment vs. openness is kind of self-reinforcing. If they're embarrassed by the question, they probably don't know much about it, and your embarrassment will be increased. If they can talk about saddle pressure with the same objectivity as they talk about your wrists, then just like disrobing for a male health care practitioner, you'll build trust and be less embarrassed to talk about your issues.