I believe the point of the Consumer Report study was to compare nitrogen filled tires with air filled tires
under the same conditions. Thus, it makes no difference whether they were under a load or not under a load if they were under the same conditions. They concluded that there was slightly less leakage with nitrogen. IMO, not enough to matter.
I know that automobile race teams use nitrogen for their tires because they do not change temperatures (pressure) as much as air filled tires.
I have my doubts whether it's worth the hassle on a trailer.
Every tire is going to lose some of whatever is filling it when it sits or goes down the road. That's the nature of the beast - especially given today's quality control on rims, valves, and the tires themselves. If nitrogen is your thing, that's cool. When you top off your tires at the start of a trip or mid-way through the trip, unless you can find nitrogen to fill them, you've just pee'd away what ever you paid for the initial nitrogen fill.
It's your money.