You will need to add a visability perameter to each door panel (on - off switch). Then create each type with appropriate panel switched on and others off. I will post an examle family later.

I did a quick test on this...If I start with a blank door family from the template, load in my panel family, apply the family type parameter and then load in another panel family, I can easily switch between the different types and different families. As soon as I try to constrain one edge of the family, I can no longer switch between families. Even if the families have the exact same ref. planes, origins, and parameters. I've attached the test file that just includes 2 panel types. if you have no constraints, they work fine, even if you align and lock center (left/right) ref. planes, it is still fine. It will break if you try to align the face of the panel to something...
My goal here, it to have one door frame family that is parametric, that I can then load in different panel types, similar to real world conditions where you'll have one size hollow metal frame, but multiple panel types that will fit into it. I want users to easily create additional panel configurations and load them into a project without having to create and entirely new door, or add additional visibility parameter to the existing, or have a ton of different door types. I know, I'm asking for a lot, but I really feel like this should be doable without a tone of headache.

I do not have Revit on this machine, but your initial aproch with "family type" parameters was right. The panels needs to be build with instance paramters for the Panel Height, Panel Width etc.
Then when loaded into the parrent (frame) family, you need to tie those instance parameters to similar parameters in the parrent family (You do that by selecting the child (panel) family > Properties > Select the little "square" to the right of the instance parameter names, and select the matching parameter in the parrent family) :beer:

Woah woah woah. No you dont.

T1shep- It works exactly as you are expecting, but its VERY VERY finicky about getting all of those constraints and parameter ties EXACTLY the same between each family. So if you build the parent DOOR with "Panel 1" which has a parameter "Height of glass lite" in it, and you tie that parameter to one in the door family, if that parameter isnt there in Panel 2, youre in trouble.

My advice?

Make one panel. Load it in, assign the family type parameter to it. Open it, save as. Save as. save as. Until you have enough copies to make your library. Do it all in one sitting. The moment you take a break, you come back and do things differently. In EVERY one of those duplicates, if you have to touch a reference plate, or a dimensional label... Youre doing something you shouldnt.

Thanks again everyone. I edited my post, but for some reason wasn't saving the changes while you all posted replies.
Here's what I discovered...
The issue I think I was having (I understand the need to link parameters in the nested family to those in the parent), was that the reference plane in the nested family I was trying to lock to a ref. plane in the parent, was also a driving a shape handle in the nested family. So even though the nested families have all the same origin planes and parameters, and those parameters are linked the same, the parent family would break the constraints. I found that if I locked the centerline ref. plane my nested families behaved as expected and will switch families without issue. I think because my nested panels have an equal constraint about the centerline, that is the only ref. plane that stays consistent between families, regardless if the origin planes and parameters are the same. Do you follow?

While there may be some room for error, what I've done instead of the save as, save as...is to take that initial panel with the base parameters and make it a family template type. So that way, when a user needs to create a new panel type, they can start from the template, which includes the base panel solid, and create additional lites, recesses, molding, etc. for their specific needs. I think we should then be able to reduce the errors when loading the new panel into the project.

Ok today wasn,t wasted learnt somthing panel type. I looked at your door and noticed you hadn't locked the origin of the panel to or "tied" the height, width perameters correctly. Got it to work but don't have time to check all peramaters.

Here's a video (no sound) that goes through what I outlined above...that essentially it was the ref. planes and constraints and parameters that were causing the issue. I think it sort of comes down to anchor points and that regardless if your parameters and constraints are identical between nested families and you know you'll never make them different, the fact is that at some point they could be different, and in this case the only ref. planes that maintained consistency were the center lines.
http://www.screencast.com/t/k28beCF4

Ok help !
Funny this post came up when it did, I was doing the same thing just a couple of nights ago. I thought I had it resolved with my visability trick but Aaron you say its the wrong way to go.
I have 3 panels nested in this door family and can change them in and out within family editor everything flexes, but how do I get to select the type once loaded.
I have always run with these doors as seperate families with a catalogue for sizes.