"power buffer" in front of generator for peak power shaving?
Buy a (petrol-fired) air compressor and pneumatic tools, or go for a bigger generator. (Good) Inverter can cost nearly as much as a generator, also remember that an inverter rated for 2kW has a substained rate of about half. I found on Amazon this 3kW inexpensive inverter, check if it may be good for you. Anyway, with an inverter it's important that the battery can provide all the instantaneous power needed, and also that the wires are thick enough: 3000W@12V -> 250A it needs really big wires (60mm^2). Also remember that motors may require a start-up current that can be more than 7 times the 'rated'.