I will join longneck, you need to give to give this one to a pro.
If you do not understand about back-feeding a circuit, already, it is too easy to kill someone. I say this without exaggeration.
The biggest problem with running a generator with a transfer switch is that you have to wire it into your main panel.
For basic protection of life, (as well as the law,) it must NOT be possible to have your generator and the power to your house on the same wire, at the same time.
This is not a case of, just for a few seconds, or I would not do that, or I will triple check a written list.
It must not be possible under mechanically, electrically, on with quantum physics.
The reason is that if you put power on the 'dead' wires to your house, it is possible to kill someone a mile away, or more.
Emergency workers expect down lines to be dead. Yes, they do check first, but that does not mean that the situation can not change while they are working on them.
Transformers work backwards, low voltage at your generator (240) quickly becomes high voltage (thousands).
And sometimes people, and pets, or cars, just do not even see a fallen power line.
This is a case of some money to a pro vs life.
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
Don't worry about it
Breakers have a certain latitude to them, and can run slightly above rating for a short time. That provides for motor starting and short term overloads.
You're not supposed to plan to overload anyway
You should be provisioning power for 125% of what you expect to actually draw. So if you plan for 6800 VA of actual load, you should provision at least 8500 VA of supply. So don't aim to draw more than 6800 VA.
If you actually have 8500 VA of load in mind, then provision 125% of that or 10,625 VA.
VA is not quite watts
Often loads don't use the entire sine wave. The part they use is measured in watts. But the entire sinewave must be generated, and that is measured in VA. This can bite you.
Anyway, it’s really hard to load the generator evenly
North American 120/240V comes in two poles of 120V each. Each one has its own breaker trip, but they are common-trip, so the breaker will trip if either side exceeds 30A by enough margin or time.
That means you must full balance your 120V loads to get full performance out of the generator. This is hard to do. I would say impossible without ammeters on both legs, and even that is not telling you about the difference between watts and VA.
If you find that issue objectionable, you can fix it by putting a 10 KVA transformer in front of the transfer switch. Now 120V loads will evenly load the generator, since the transformer is balancing.
Never parallel
Electrical connections should never be paralleled, except in certain rare instances. There are many reasons for it, including eddy current heating, but one problem is neutrals. Current will flow as it pleases, while completely ignoring any breaker trip ratings. If your breakers are 30/15 it will cheerfully flow 39/6 if it wants to, and trip your 30A breaker.
But much worse is happening on the neutral. With two competing neutral route, the same thing could happen and neutrals don't have breakers. So you're just setting the wires on fire at that point.
Even when paralleling is done industrially, special equipment is used which deals with this important point!
Suicide cords, never
I have done some janky things with power. But making a cord with males on both ends is something I would never do. No problem exists which requires that as a solution.
Firstly you have the problem that you will inevitably have one end plugged into "live" while the other end is free to contact anything or anyone.
Second, you have the problem that a suicide cord can do an end-run around your transfer switch/generator interlock. That can be over to "utility" side while your suicide cord backfeeds the grid. This defeats the purpose of having an interlock.