Safely run the microwave for an extended time with just a bowl of water

Microwaved eggs was probably one of the first things that I learned to cook -- I don't know I'd consider it an 'omlette' necessarily -- it was just a bowl, oiled, broke an egg in it, a touch of milk or water, mixed, and then microwaved.

When you're rushing to get out the door in the morning, it's a dead simple breakfast; I was recently out of town, and the place I was getting my breakfast in the morning (a bagel joint) did basically the same thing -- put a laddle of egg into a container, microwaved, put it on the bagel, and you were out the door.

Personally, I'm of the opinion that velvetta melts at a low enough temp that if you're using the pre-sliced stuff, you'd probably be okay just cooking the egg, putting the cheese-food on it, leave it in the microwave (off) for ~30 sec, and it'll have started to melt.

(but then again, I like to know cheese is there ... not be some runny molten filling that runs out when you're eating something, so I don't want it too melted)

1100 Watt means 1100 Joules per second (energy over time). 1100 Watt over a period of 240 seconds therefore is 264000 Joules. To deliver 264000 Joules of energy with only 800 Watt takes 330 seconds (5.5 minutes), as you expected.

As KatieK noticed, there are some additional concerns. A good recipe will tell you to let the cooked product stand for a while. This allows heat diffusion, so all those Joules of heat will be distributed well. But if you cook at lower power, then the heat will already be diffused more. I.e. at lower power, you don't need to rest the product as long.

Another difference might be that you're not just heating the product, but you're relying on a secondary effect such as killing germs. For that, you'll need to have the entire product above a critical temperature for a certain time. This in general means that you don't need to adjust the times as much as you'd expect by the simple formula.

On the other hand, a warm product will lose heat to the environment over time. I.e. not all of those 264000 Joules will stay in the product you're heating. And with more time spent at medium temperatures, there's more heat loss in a low-powered microwave.