Designing a Smaller 2000W Transformer PCB to Run 220V Heating Element on 110V
A two thousand Watt transformer is going to be big and heavy. For AC conversion the transformer is a good way to go though. They are efficient and produce real AC waveform outputs.

It is possible to envision a design that would convert the voltage by rectifying the input AC to DC. That would then be converted to a different voltage using a high frequency switcher design and then synthesize a fake AC output. Such device would not be trivial to build however but it could be smaller due to the smaller magnetics required.

Personally I think you would be way better off to set your 220 volt heater aside and get a replacement product that is designed from the outset to work on 110V. And surprisingly that may even cost less.