How do I adjust cooking time for an under-powered microwave?

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.

There is no simple math equation that will always get you the proper cooking time. Each 800W microwave may differ, even within the same models, due to hotspots.

You can estimate that a 800 W microwave will be 72% as effective as a 1000W model, and that you want to increase cooking time to about 5 minutes. But since you can't fix over-cooked food, check your food early, and check often.