If you are getting custom cabinets I believe your cabinet maker could provide a solution for you.

For that cabinet they could create a fixed shelf at top then ducting could be run through to the side of the cabinet. In the side they could create a custom wood vent simply by cutting thin grooves in the side in the same direction as the grain of the wood. (be sure they do this before applying the finish) I believe the result would make the vent barely noticeable.

If seeing the duct work when you open the cabinet bugs you they could build a removable panel that fits in front of the duct work to hide it.

Will your new cabinets be going to the ceiling w/doors or just "wall" even with the front of the cabinets? Other?

Basically, pretty much any register -- supply or return -- can be taken off and another straight length of duct added and a new (or newly painted) register grill added to the extended duct. Too many curves added can impede air flow.

I adjusted the ducts in my house and put it in the ceiling

Can you move it to where is comes out of the ceiling like most a/c vents do?

I don't know what added expense might be, but the HVAC people put mine in the toe kicks when changing my system. I especially liked the one at the sink. Warm feet in winter and cool in summer....

Where is the furnace? Basement? Attic? Utility Room on 1st Floor? That will dictate the relative ease of relocating the duct.

Furnace is in the basement. Options for the duct would be extending it thru the ceiling to the front of the cabinet or fridge, or turning it 90 degrees to the left or right. There’s enough depth to put a panel in front of the ductwork with an over-the-fridge cabinet.

id rather go stock cabinets if I can, but it would be possible to put a slotted or mesh grille in the cabinet that’s not too noticeable.

if we leave the fridge in it’s current location, I’d do a pantry cabinet here with a toe-kick register.

If the duct is coming up from the basement and you have clear access then relocating the register should not be difficult. If you are installing a base or tall cabinet below the register then the duct can be installed in the toe kick. I had the same issue during my kitchen remodel. The heat coming from the toe kick actually is a better placement and less costly to move then having it high up on the wall or ceiling. If the refrigerator is going in that location then a floor register would work. I would locate near the wall and corner so you don't step on it on a regular basis.

"if we leave the fridge in it’s current location"

I wouldn't. It must be difficult, or impossible, to open the left door all the way to pull out a drawer.

Since you are on a basement, can you put it in the floor?

You could have that moved down the wall and have a toe kick vent.

That depends whether I put a full-height pantry cabinet there, or move the fridge around the corner. With the fridge there, I have to go above, and out the front, right or left.

To Jake - it's possible, but the joists run 90 degrees to a desired direction. I'd have to put it in the middle of the hallway / kitchen transition if it's in the floor.

Shannon_WI

"if we leave the fridge in it’s current location"

I wouldn't. It must be difficult, or impossible, to open the left door all the way to pull out a drawer.

The wall section there is 40" from the door trim to the stub wall, so there's plenty of room to do a 36" pantry cabinet with a trim strip for any offset needed. Same with the fridge - 40" gives room to trim it out on either side. Right now, I have a 30" deep KitchenAid SBS that I don't want to get rid of until I have to. It's 16 years old, but still operating fine. Once it goes, I'd switch to a counter-depth in either location.

Have the vent come out directly below at the Toe Kick.

Should be easy.