Remove hot air from sloped ceiling to attic with exhaust fan

I have what I think is an unusual setup of a sloped ceiling that may offer an easy fix to my problem, but wanted to get some opinions from you guys.
Our master bedroom, on the 2nd floor (top floor), has a sloped ceiling (roof above it) and also a wall that is 2 stories high. So it's a square room except 1 wall is 2x the normal height, and therefore the ceiling is sloped. The master bedroom faces west, has a large window on the short wall, and gets pounded with sun all afternoon. It gets up to about 80-82º. It's nearly impossible to get it cooled back down with the existing single duct. The upper part of the tall wall has an unconditioned attic on the other side of (behind) it.
The 2 other bedrooms on the 2nd floor have normal flat ceilings, with the attic above it. Those 2 other bedrooms are facing east. They stay nice and cool in the summer.
About 5 years ago, we had new insulation put in the house: loose fill in the attic, and dense pack in the master sloped ceiling. They did not install air ducts (baffles?), so I think the insulation is just really packed in. Worked well for keeping it warm in winter. But now it's not in summer.
I've tried adding an in-vent fan that constantly pushed air in the room. That helped a tiny bit. I installed a blackout shaded, which keep the light out well, but has not helped the heat build up.
I'm having some HVAC people come to give their opinions on what can be done, but I wanted to get your thoughts.
*One idea*: add another duct from the basement blower unit up to the master. This will be costly I'm sure. Will this help solve the issue?
*Second idea* (maybe a bad idea, I don't know, please tell me): The upper part of the tall wall in the master has the attic on the other side of it. So, would it make sense to install a simple bathroom exhaust fan high on that wall, that sucks the hot air from the top of the room and dumps it into the attic (or out to the side of the house)? With the attic setup, looks like it would be easy to install and hook it into a light switch in the master bedroom.
That unusual setup of the high wall that has the attic on the other side of it - seems like a good opportunity for a simple, inexpensive fix to the problem (exhaust fan). What do you guys think?
Any other thoughts about options that would be most effective in getting rid of that trapped hot air?
Thank you!!
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