Cost of doing business. You are not going to get any money for it. It sucks, but that's what it is.
Basically, I try NOT to take assignments that I cannot do repeatedly and that are profitable. I do not want to bother learning/preparing for a 1x or 2x shop. I'm not saying this oil change shop falls under this.
This sounds like the Chrysler oil change shop to me. I would not take my Honda to a Chrysler dealership to get an oil change. Just seems goofy. Especially in the Los Angeles area when there are plenty of Honda Dealers to visit.
There are oil change shops for Jiffy Lube and other non-dealership oil change shops available if you really need an oil change and want a shop for it.
In addition, I would never "set aside" a day to do something like this. I get the people who shop full-time for a living and setting up routes. That did not sound like your situation. So I am not sure what "set aside" means in your case. I shop and make my shops fit into what I'm already doing or where I am already going. I don't make special trips/visits just for a shop UNLESS it was a huge bonus and it worked out for my schedule. I make shops fit into my routine/schedule and those that don't, I won't do.