I doubt they will want to upgrade hardware on their dime, you aren't a typical customer. If you were to move they would have over built, under utilized infrastructure. Time to look into commercial/industrial locals.
if you have city approved permitted 200 amp service you are entitled to use it.
now following the very conservative 75% constant run safety margin you are allowed to pull 150 amps 24/7/365. that would be 18000 watts non stop.
of course your problem may be the city/town did not permit 200 amp service or you may draw more then 150/200 amps.
good luck fighting them.
put another way " if you are using under 75% of your permitted amp rating 24/7/365 you should be allowed to get that. "
Ask the power company to show you in writing that the statement above is wrong. if you are in an area wide power shortage brownout they can shut you down.
but in non emergency conditions they should be required to provide what your city/town permit rates your home for.
My home has 150 amp 220 volt service which is split into 2 110 volt rails. other then one 40 amp fuse for my ac at 220 volt.
I run 6000 watts 24/7/365 for mining in the winter and about 2300 watts in the summer