As has been discussed many times in this forum, back feeding a generator into a double or even a single pole breaker without a transfer switch is risky business. If the main breaker is not disabled while generator is online, you will be back feeding power to the grid and pose a safety hazard to utility workers.
With that said, look at the following link, http://www.southwire.com/support/voltage-drop-calculator.htm The wire size for an 80 run at 30 amps/120vac is 8 AWG. Use this calculator to determine wire size or determine voltage drop. 3% drop is usually considered max for 120/240 runs. Once you start to draw amperage, the drop can become greater as you tax the voltage source with a fixed or max amp output.
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
Running the house off the L6-20 receptacle (without the neutral) would be almost sure to start wrecking things on your 120V circuits in short order, blowing light bulbs, refrigerator, etc. And at the worst possible time, during some emergency.
Since there are 120V receps you know there's a 120V tap in there that can be used to supply line-to-neutral loads. However there's a chance it is too small to carry the full neutral load for this application. I am not sure, but from that wiring diagram but it looks like the neutral tab on the 120V receptacle is the neutral-ground bond.
I think it would be possible to modify the wiring and install a L14-30R receptacle, but it wouldn't be a modification I'd be comfortable making. The alternative would be to use a transformer between the generator and the backfed breaker, but at that point maybe you just buy a different generator better suited for the application .