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I would like to remove the soffits in my kitchen. However, an a/c vent approx. 6 inches wide perpendicular to upstairs floor joists (2 x 8s) runs the length of the kitchen. This vent cools/heats two rooms upstairs. Any suggestions?
The question is not clear regarding where the soffits are in the kitchen ceiling. But unless you want the supply duct exposed, you will have to re-route it to feed the 2 rooms upstairs.
Looks like you're between a rock and a hard place. Assuming your house is an older one, rerouting parts of the existing hvac system is going to cause more problems than it cures. Unless you have tons of money I'd advise you to make the soffits look good, possibly by installing low voltage halogen accent lighting in them, and after a coat of fresh paint leave them as is.