Can I run my 40 Amp Range Stove partially on a 30 Amp generator

Generally yes can use part of your range. Each burner is different, I've seen 8" burners use up to 2500 watts, smaller can be 1200 to 1500.

I have even baked a pie. However I had to trick the oven by preheating on the broil setting since preheating on the bake setting uses both top and bottom elements and my biggest generator is a 5500.

I would seriously rethink this. Electric stoves are wonderful. But they use a lot (relatively speaking) of power. Unless you expect long term outages, a far better solution is to get a cheap 120V 15A microwave oven. It will draw 1500 W or so when running but that will let you run lights, refrigerator, etc. at the same time. For a day without power, reheating stuff, or even some very basic cooking will get you through. Can't bake a pie or broil or fry eggs, but you'll still be able to eat hot food.

I'd take a third option here. You clearly have a place to store fuel and someplace where you can run it so I would suggest a propane tank and stove. Cheap, very long shelf life so long as it's stored shielded from water. (The propane lasts forever, the tank can rust. Note that the tank has a 12 year expiry date--you won't be able to refill it after that, but what you have in it will still work.)

You'll get a lot more cooking per pound of fuel and you very well might be able to use a smaller generator.

You are good as long as both the generator and the stove users are more or less sane. Well, if one makes a mistake to turn on more stoves than the generator can bear, the generator will have to be reset, bonus if it is at night.

I am yet to see a generator that breaks when overloaded. Most of them brownout (if the overload is mild) or just trip their breaker.

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We have quite a similar problem here.

My wife ordered (and received) a cooker. The required total power happened to be crazy - 8.3 kilowatt total, 36 ampere at 230V (Europe here).

Wires in the kitchen are good for 25A only, the landlord is OK with us upgrading them, but for one reason or another it will not happen soon.

So the temporary solution is not to turn on all 3 ovens at once. Failing that, the breaker trips. My wife is OK with resetting it once in a while.