A paper written by D. Ludois, J. Lee, P. Mendoza, G. Venkataramanan suggests that adapting a MOT transformer for other use could benefit from removing the magnetic shunts and the filament winding and adding about 10 turns to the primary. There may be information on the internet that shows how to do that. Look at:
Reuse-of-Post-Consumer-E-Waste-for-Low-Cost-Micropower-Distribution.pdf
Adding turns will reduce the magnetizing current, the cause of the problem. The primary current is high because the MOT design causes a high degree of iron saturation. Adding turns also reduces the secondary voltage slightly and increases the secondary current for a given primary current. Reducing the magnetizing current reduces the losses making the transformer run cooler for a given load current or allowing a higher load current without overheating.