You absolutely can stack inverters. You just have to have a model that is designed for it. I don't think the OP's inveter is so he would need to buy 2 120v inverters that will stack. Outback FX series will. The older Xantrex and Trace DR and SW series will do it too. Also the Magnum MS4024.You cannot stack inverter outputs! There is no way to control the frequency and insure that they are always in phase with each other.
The only two options for 240v for an inverter are a transformer or 240v inverter output. You can get a 240v inverter or just stack two compatible 120v units. Outback, Xantrex, and Magnum all make very nice 240v output inverters. However, it's probably less expensive to keep the one you have and add an autotransformer. Outbacks should work fine. It's heavy but so are batteries and inverters.
Heat is heat. You can't use less electricity to get the same amount of heat no matter what type of cook top you use. Cooking with electricity will take lots of battery power.