That is an old "rule of six" panel, which while grandfathered, is illegal under its grandfathering becuse it has 7 main breakers. Going to five is a good plan.
It is a classic "CH" panel which is a very good industrial grade panel, except that the 3/4" breaker width make non-ordinary breakers very expensive (a trait it shares with Square D QO). That makes it perfect for what you plan.
On your subpanel which would be near this panel, I would get a panel with a main breaker, with an eye toward (at some point in the future) cutting it over to be the main panel. In a subpanel, the "main breaker" is nothing more than an on/off switch, it is OK for it to be larger than the feeding breaker.
I would also get a rather large panel, at the very least 42 space and even 60 or 84 if practicable: because panel spaces are dirt cheap and often even come with free breakers, whereas running out of space is painfully expensive.
I would aim for an industrial grade panel of good repute (one available in 3-phase variants, not Homeline, BR, or second tier brands) and avoid the expensive 3/4" breakers (not CH or QO).
Over time, as you find it convenient, i'd migrate all your 1-pole and smaller 2-pole circuits over to the new panel.
For your garage panel anything would do, but I'd go for the same type as your indoor panel, so you can use some of those bonus breakers. Again it's false economy to scrimp on spaces, I'd go 20-30 at least.
Also, since garage spaces need to be on GFCI, consider getting a subpanel which has a "main breaker" which is GFCI, that way all the breakers in that panel would be protected (at the cost of potential nuisance trips, a big deal if you keep a freezer in the garage).
Ed Beal raises some very good concerns about overall capacity. One problem with these "rule of six" panels is there is literally no main breaker to stop you from drawing more than 150A. So it pays to be conservative.
It's a difficult situation because you have two big loads that operate sporadically - the EV charger and the range. And the A/C as a wildcard.
One thing I might suggest, is feed the garage subpanel from the new primary subpanel. And then move everything but the range over to the new subpanel. At that point the only things still in the CH panel would be a 60A range breaker and a 100A subpanel breaker. Even at max, those two could not overload the 150A service (by enough to matter). This would force your entire house (from A/C to EV charger) to share 100A, but would remove the possibility of an overload. This would also save you the $85 you'll spend on a second 100A CH 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
You know your approach is wrongheaded and dangerous. But that's also because it is not necessary.
We'll do my favorite trick: Permanent wiring methods temporarily. In other words, wire it up all Code legal like it'll be there for 50 years, and then 50 hours later, undo it.
It is perfectly legal to install an inlet on your home that powers any number of outlets in your home. It's also legal to use flexible cord for the inlet, if it's to be frequently unplugged.
Going into your heater socket is bad because there's a thermostat in the way. So instead, we'll go into the thermostat location. But hold that thought.
Rewiring the service panel
First, in the panel, we take some photos (this can be done well in advance), and identify the circuits we want on generator backup. We also identify the fat 10 AWG cable going to the heater. It'll have a black and white wire. We take the black wire, and join it to all the black wires from each of the circuits we need to power on generator.
Now here's the tricky part: we follow each circuit black wire, back to its cable, and identify the white wires also in that bundle. We pull those off the neutral bar, and join them to the white from the heater. Don't just leave them all on the neutral bar; pull them off. This is important, because the generator GFCI will trip if you don't.
If any of these cables have a red wire also, you need to figure out whether you need red or black, and connect that one to the black bundle. If the wire is 12 AWG, you can just connect both to the black bundle.
At this point, none of the wires for the heater circuit or desired circuits are on breakers or neutral bar anymore. They are nutted to each other, using the service panel as nothing but a splice box. This is Code legal.
The ground wires, leave them where they are.
At the thermostat
Now, back at the thermostat. Open up the thermostat, take photos of the existing wiring as-it-is. If you feel it'll help later, mark some wires with tape before taking the photos. Now, remove the thermostat, and store it.
Now, we need a heavy duty 12 AWG appliance extension cord. Oh hey, that suicide cord you already faked up needs to be destroyed anyway... so let's kill two birds with one stone. The 240V (NEMA 6-30) plug you added -- remove it. Get to black, white and bare.
Now, get an appropriate blank cover plate for the thermostat box. Except we need a cover plate with a knockout on it. We also need a proper strain relief for that cord; an electrical supply house will have no trouble setting you up if you bring in the cord. Install the cord in the blank cover plate, with the strain relief, and secure it.
Now, in the thermostat box, identify the cable that goes back to the service panel (not the one going to the heater). With those wires, splice cord bare to cable bare, cord white to cable white, and cord black to cable black.
Install the cover plate and screw it down. Now you have a flexible cord coming out where the thermostat had been, with a plug on the end. This is a code-legal inlet.
The use of a flexible cord is legal because this will be connected and disconnected frequently. As in, twice.
Once the crisis is over, rollback the wiring to the way you found it. Take the cable-with-cover-plate-on-the-end, and throw it in the emergency kit for next time.
The one Code problem here
Presuming the generator's circuit breaker trips at 20A, we may be connecting 14 AWG /15A circuits to a 20A breaker, which would violate NEC 240.4's statutory limit of 15A on #14. (thermally it's allowed 20A at 75C temp). However, the practical likelihood of overloading them is low, since you'll be powering several circuits off one 20A breaker, and it's unlikely for one 15A circuit to gobble up more than 75% of total available power.