Microwave transformers are cost optimised.
They run at high magnetisation current so that the core material is "very well used". Removing the shunts, as you have done, is a good start.
Adding more primary turns may be difficult with the windings that you have added, but, given that you have the now removed shunt volume to work with, this suggests that you MAY have more copper and/or winding area than is strictly needed for your task.
Presumably it's not a 60 Hz transformer being run on 50 Hz - which would add handsomely to your woes.
Ensure that you have minimised core air gaps.
Presumably the laminations were priginally welded and you ground off the welds?
Ensuring that the two parts of the laminations are in intimate contact is "a good idea".
A method of ensuring good clamping force is in order.
Added 2022:
uWave transformers are driven VERY hard. Heating results. Adding 10 turns to primary reduces core flux and saturation. Removing magnetic shunt (funny metal bridge in winding space) helps. 10 turns added to primary can be anywhere in winding space and added in series to current primary winding.