I'm sorry, but both of your towing options would require you to significant overtow the weight limits of your car. The 1st option would actually have you towing a load that is heavier than your car and would make it quite literally impossible to control. You would be a missile coming down even the slightest of incline, much less the roads you'll have to cross getting through the rockies. Please, do not under any circumstances consider that as an option.
Your second option is not much better, as the empty trailer is already at or near your maximum towing capacity, and it doesn't take hardly anything to put 200 pounds in the trailer. In fact, if you are looking at a trailer to pull just 200-300 lbs of stuff, then it would be vastly more economical to ship that stuff, be it with uship or even with UPS/FedEx.
I will say that your fuel cost estimates seem extremely low, as I don't think there is anyway you will be getting anywhere near 20 mpg, much less 30 mpg, when pulling that kind of weight. I would also be budgeting a significant sum of money for repairs because of the extreme load you'd be placing on your vehicle.
Route-wise, weather will be something to keep an eye on. I-90 stays generally at a lower elevation than your other options. But I have to say, based on what you've come up with at this point again, I would urge you very strongly to give up on the idea of towing with your Yaris. You won't be saving any money if you crash the car, or have a burned up engine/transmission when you arrive in Oregon.