Which panel to add second solar system

TexasTom

I have a leased, all paid upfront 6.44 kwsystem feeding into my main 200 amp panel. no modifications allowed.
I want to add a owned by me second 5kw inverter and panels.
my service is underground to an outbuilding on the property with a dual lug 320v meter box.
one side of meter feeds a 125 amp box for the outbuilding with very minimal power use
the other side of the meter feeds into a generator transfer switch then to the main house and another outbuilding.

the only way to add more solar to the main panel would require reducing the main breaker size, so the question is..

if I add the new 5kw system to the 125 amp panel on the outbuilding that currently has no solar feed will the solar power it makes in excess of the outbuildings actual use go straight out to the grid or will it offset the power that the house uses from the other side of the meter ??

hope this question make sense... here is a picture of the meter withy 125 amp box on right and transfer switch going to house on the left