I've actually done a simplified version of this experiment before, so I think I have an idea of what the problem may be. There are a couple of things that you could try.
First, water doesn't change temperature very easily; its specific heat is very high. To increase the temperature change, you could try reducing the amount of water. This wouldn't mean that you would have to do all of your trials over again- the amount of water would end up canceling out the temperature change in your calculations- but might help your accuracy and make it easier to measure.
Second, looking at the design of the experiment, it seems to me like there are a lot of places that heat could escape without going into the water. You could try putting the can closer to the flame, if possible, or you could try to cover up the open top of the larger can with something nonflammable.
As for catching the food on fire more effectively- a lot of foods, including marshmallows, are a little moist, and may stop burning before all of the calories have been released as heat. To help increase the number of released calories, you might try to light the entire outer surface of the marshmallow on fire, instead of just starting a fire at one place. If that doesn't help (or you're already doing it), maybe you could try to find some larger marshmallows? Those would release more heat, as they contain more energy.
If you have any more questions, or something was unclear, don't hesitate to ask!
Good luck, and I hope this helped!
Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.