I'm a cheese lover. But there are times I've had cheese platters (not at WDW) that had cheese I did not care for.
I've looked at the various restaurants that server the cheese platters and many of them only list 'artisanal cheeses' which could be anything as long as it's a small production cheese.
Of the cheese you've mentioned, you're not likely to find many of them on a cheese platter. Brie & Camembert, possibly. Cheddar, maybe -- especially at Rose & Crown b/c of the various great English varieties.
I think your best bet might be to try a good variety of cheeses BEFORE you go. Go to a place like Whole Foods that has a large cheese section and ask for samples. If you have a nice cheese shop in town, go there. Explain to the person working there that you're trying to expand your cheese likes and would like to try some new/different cheeses. You will be pleasantly surprised!
Cheese platters are set up differently, depending on who is putting it together. At a restaurant, it can be regional cheese -- so any type of cheese from that region (England) or by type of milk (all sheep milk cheeses). Normally, you'll get a hard cheese, a soft cheese and a sharp cheese. But having never had one at WDW I can't speak of those restaurants. Hopefully someone who has enjoyed them can chime in.
Some really great cheeses to try are:
1. traditional chevre (goat cheese) -- soft and sharp
2. Manchego -- great hard cheese from Spain, mild, flavorful. It is a sheep-milk cheese
3. Fontina -- soft, smooth, reminds me of havarti
4. Asiago Fresco -- it is the soft version of Asiago which is a hard cheese. I like the Fresco b/c it is soft (like a havarti) but packs a lot of flavor and is not over powering
5. Gouda -- soft-ish (a little more firm than havarti), flavorful
I love trying new cheese that I normally wouldn't buy. It has been a great adventure with my daughter, who thinks a store w/o cheese samples just isn't any good.
Don't be afraid to try the cheeses. If you have give things a try and just don't like any of the (i.e., blues) then let the server know. I have a very good friend who loves cheese but is highly allergic to veined cheese so he has to let servers know this when he does a cheese course. WDW is a great place to have an adventure. And, if you just don't like any of them at all let the server know and I'm sure they'll try and figure something out.
Best wishes!