You will get more current if you have an air gap. The frequency is fixed, and the saturation level of the core is fixed, so the back-emf from the winding only depends on the number of turns. If that is less than the supply voltage, you will get a lot of current even with no load.
I suggest that you add a few more turns on the primary. If you are using second-hand microwave transformers they should be cheap if not free, you could find two identical ones and put the primaries in series. If you make the secondaries identical, and put them in series, you will be running a long way from saturation.