Ive been trying to brainstorm this as well. Little different setup than yours but the idea is the same. How to get cold air to the area that is warm.
Is $40 in materials reasonable? Do you care if 4" flexible ducting is hanging from your ceiling?
One idea is to use a 4" blower fan matched with 4" ducting. You can either suck hot air, or blow cool air.
The easy option is let the ducting sit on the floor. Blow cold air to where you want.
I wonder if the more effective option would be to suck the hot air out. You would have flexible ducting hanging from your ceiling. The blower would suck the hot air out of your bedroom, and blow it towards your a/c unit. YOu could even have the flexible ducting terminate right into the intake of your a/c.
That would evacuate hot air from the bedroom while sucking in cold air from the main room.
I dont think closing a vent is helping. Keep all vents open so the a/c can breath. Use fans to circulate the air.