@CobaltNinja
I've got a thread of my own somewhere around here where I'm experimenting with zone overlaps. I haven't gotten to the guildhall/hospital attempt yet, though that's definitely one I want to try out. Here is what I've found so far though:
If you overlap Zones (these are the areas you create directly, like a pasture, or a meeting zone, a dining hall, a bedroom etc) then the value of all the zones that have floor tiles that overlap go to ZERO. Even if they don't fully overlap. (they can share walls and doors though) For this reason I've currently decided against overlapping dining halls or bedrooms with any other zones so far, because the value of dining halls and bedrooms matters. The value of a pasture or meeting zone might not matter though, which leads us to...
Locations (the things you can attach *to* zones, like hospital, guildhall, tavern, or temple) can not share a Zone (e.g. you can't have both a hospital and a guildhall attached to the same zone). But if you overlap Zones, you can also overlap Locations. As I said above, the value of the overlapping Zones will go to zero --- but the value of the Locations is fully retained.
So for example let us say you have multiple overlapping Meeting Zones and you assign a different Temple Location to each of those zones. The meeting zone value is zero (not that you can *see* the value of a meeting zone anyway) but each temple has the full value. So you can definitely have all your civilization's religions overlapping in the same room!
And value-wise, that *does* work. However! I've noticed some odd behavior I'm still trying to work out. It *appears* that when you overlap Locations like this (e.g. multiple layered temples, each with their own zone but overlapping) the dwarves only USE one of the Locations (in theory, the first one placed.) I'm doing some experiments to see if they can use both locations if they don't fully overlap, but not conclusive yet.
So for your scenario CobaltNinja, it looks from your screenshot that your meeting zone is separate from the dormitory zone (e.g. they don't share floor tiles)? If that is the case you should have no issues with assigning a Hospital Location to the Dormitory Zone and a Guildhall Location to the Meeting Zone (though I've never linked a Hospital to a Dormitory before, interesting idea!). In this situation they're not actually overlapping at all so both of them should be used just fine. You could even expand your Dormitory Zone to include the walls and doors (but not the floors) of the Meeting Zone, if you needed to increase the value of the Dormitory Zone/Hospital.
@Blue_Dwarf and @Metruption - you can not attach both a Guildhall Location and a Hospital Location to the same Zone. You can however create two overlapping Zones and assign one to the Guildhall and one to the Hospital (with the above warning of what I've seen about dwarves only seeming to use *one* of the locations in my testing so far). Since they're attached to separate zones, a member-only guildhall shouldn't prevent any dwarves from using the hospital that need to, but the whole 'using only one of the overlapping zones' might cause interference whether they're members-only or not. It needs some more testing though to prove it out.