You're looking up parts with the wrong terms. What you want is a transfer switch. You don't need the kind that includes breakers, etc., since you're using an interlock; just a simple transfer switch.
In a transfer switch where the neutrals are bonded or overlapped during switching, the advantage is reduced arcing and transients during switching. The disadvantage of this situation is that the transfer switch can not protect your genset and other electrical system components from wiring problems, such as a neutral/hot reversal sending current along the neutral.
In your case, since you're using an interlock you will already be cutting off the electricity completely anyway before switching and starting your generator; neutral continuity is not needed. So you should use a transfer switch that switches the neutral along with the hots.
See http://ecmweb.com/content/switching-neutral-whats-controversy for more details.
Ok you wrote a book. Proposing all manner of third rate hackery. And what does it boil down to? You want to get 5000W out of your 5000W generator. Quick question.
What is 240 x 21 ?
By my math, it's 5040. There's your 5000W. You do get it out of the big NEMA L14-20 connector.
I have no idea where you got 41A. I'm pretty sure you made that up, probably by dividing 5000 by 120. I seriously doubt it was on the generator spec. There's a way if you really really want that, but as you get educated, you will realize you do not.
What is it you're missing? The odd idiom of North American 2-pole service. I don't blame you for not getting it... It's weird.
Your house is served by +120V, neutral (0V), and -120V. I just described an instant in time, they're AC so they will reverse position 120 times a second. The poles are called L1 and L2 and the middle is Neutral.
240V loads grab L1 and L2. 120V loads grab either pole and neutral. Which pole they grab is nearly random and that's the idea, to make them average out so loads are balanced.
For you, with 21A on each pole, balancing is a big deal. You'll have a problem if you put 30A of load on one pole. So you'll need to get into the gory details of what is on which pole, and manage accordingly.
Step 1: Control MWBCs so they don't kill you
I don't recommend rearranging things on a panel because you can break a type of wiring called a multi-wire branch circuit. Find an electrician and tell him to do exactly this:
find every multi-wire branch circuit in my home, and make sure both its hot wires are served from the same 2-pole breaker.
Step 2: get rid of double-stuff breakers
If your panel is stuffed, and has lots of breakers that have 2 breakers in 1 space, those will drive you absolutely bat crazy. ack... You know what, to heck with all that.
Let's just get you a new subpanel with the appropriate interlocks, and move the loads you want the generator to power into this new subpanel. Make this subpanel quite large (at least 20 space) realizing you'll use 4 spaces just for the interlock.
In a perfect world, your new panel will have ammeters which will tell you how close to 21A each pole is getting. Even better get one of those new fangled whole house monitoring systems. Ask a new question on how to get one to work in a generator interlocked panel.
Step 3: rearrange your loads in the panel
Now finally, it's time to learn the gory details of how poles are assigned in a panel. Read my posting here. Your panel may differ, but probably not by much.
Move your loads into the new panel, and consciously and carefully balance the loads. For instance if your table saw is on L1, put your dust collector on L2. Stuff like that.
Best Answer
Assuming that your load calcs were based on actual load and not breaker sizes, the DPDT switch idea has merit. What I would look at though is the physical location of the loads. For example is your 240V dryer in the garage? If so, then I would put the DPDT switch in there to feed either the dryer or the car charger (assuming the sizes match), because you are going to manually connect the car anyway, so you throw the switch when you make the connection. It does mean not running the dryer and the car charger at the same time, but you are going to be giving up one load in any case.
What I would get is called a "Double Throw Safety Switch", like a disconnect switch except the handle is On-Off-On, as in Dryer up, Off in the center, Charger down. This is a picture of a 3 pole version, you only need a 2 pole, but it gives you the idea.