There can only be one point in the system where neutral and ground wires are joined, and this is usually in the main panel. Therefore, you must lift the bond from the generator, or disconnect the ground wire from the generator to the transfer switch.
If you lift the bond on the generator, you can run both ground and an insulated neutral back to the transfer switch. You will also run ground and insulated neutral from the main panel to the transfer switch, and ground and insulated neutral to the subpanel from the transfer switch. Note that neither neutral nor ground are switched in the transfer switch. The generator can optionally be grounded to a rod.
If you cannot lift the bond, disconnect the ground wire to the transfer switch at the generator (or don't run a ground wire at all). The subpanel will still be grounded from the unswitched ground wire from the main panel. The generator cannot be grounded to a rod because this would tie the neutral to ground in a second location through the bond.
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
2014 NEC 300.20 (A) "Where conductors carrying alternating current are installed in ferrous metal enclosures or ferrous metal raceways they shall be arranged so as to avoid heating the surrounding ferrous metal by induction. To accomplish this, all phase conductors and where used the grounded conductor and all equipment grounding conductors shall be grouped together". Also see 2014 NEC article 702.