If that is the red and black from the same 14/3 cable it is anyone's guess why they did this. In any case they are using the same circuit on both wires, obviously. If there is no problem at this time just splice the two wires to a tail of the same gauge and put that one tail on the breaker. Those GE breakers are NOT made to accept two conductors, but it's also not the end of the world either. Since you are working on it is worth fixing.
IF you do feel that stongly that you want them on separate breakers you MUST use a 2-pole breaker, and NOT a tandem, or twin, breaker.
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
To simply look at this situation and immediately call it a violation, is incorrect. While it may indeed be a violation, more investigation is required.
At the end of section 110.14(A) in the National Electrical Code (NEC), there is this short paragraph.
Which means if the terminal allows multiple conductors, it should be labeled somewhere either on the terminal itself or in the documentation inside the panelboard. So make sure you read all of the labels inside the panelboard, before marking this situation as a violation.
However, Section 408.41 of the NEC, clearly says that the grounded (neutral) terminal block is a violation.
There is an exception to this section, but it does not apply in this situation.
But wait, there's more... Section 90.4 of the NEC, allows the Authority Having Jurisdiction (AHJ) to waive requirements or permit alternative methods.
There is also 90.2(C), which may fit your situation better.
It may also be important to note, that the installation is only subject to be compliant with the currently adopted code. Which means if this was installed before these codes were adopted, this could be a legitimate installation.
The best thing for you to do, would be to contact a local licensed Electrician. Ask them to take a look, and make recommendations as to how this situation should be handled. If you contact the local electrical inspectors office. They should be able to tell you when the work was completed and approved, and by whom. They should also be able to find any special notes supplied by the inspector, that would indicate if the inspector gave special permission in this situation. If the work was completed by an unlicensed Electrician, the homeowner may be responsible for the repairs. But this would completely depend on your location, as well as many other legal factors that I will not discuss here.
Fixing this is not a DIY task.