Tldr:
Why are you putting poly? Iirc the closed cell spray foam does not require the poly before the drywall.
And I paid about the same to do my garage (double garage, $4500 incl. re-drywall ceiling)
Room is 2 degrees cooler than master as well, but it is almost 3 degrees warmer than it was.
Also, that foam prevents any air from getting into the house, so I wouldn't mess with it to add a vent.
Look into a vent booster.
Also, to answer question, I don't how much the blown insulation would help.
I also added extra batts in the attic above the room, and but those rubber fin things around the garage door. Insulated garage door will help also.
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