Unfortunately I can't recommend a specific refrigerator for you. But I wouldn't want to waste that 6" either. I have counter depth Sub Zeros at home (36" wide, one all freezer, one all fridge). At my vacation home I purchased a standard GE refrigerator and since the kitchen is small we recessed it a few inches into the wall and built out the one cabinet next to it a few inches. There are cabinets above it and on the outside is a floor to soffit panel that matches the cabinets. It certainly isn't the same look as my built in Sub Zeros but you sure can't beat the price and the look isn't bad at all. Most of us grew up with standard depth refrigerators and I don't think you'd lose track of items that are in the back. Plus you can still fit a large pizza box or large serving platters in them- and they don't fit in a counter depth unit.

We just installed our kitchen aid counter depth frige. It does not have counters next to it but rather pantry style cabinetry (which are standard depth). It looks like it sticks out about an inch or slightly less than I want it too (not the doors or the handles but the body of the frige). Once the doors of the cabinets are installed it shouldn't be as noticeable. My cabinet guy did recomend to notch out some of the sheetrock in the back of the frige where the plug is (because the stiff cords are preventing the fridge from going all the way back) and it should fit even better. The kitchen aid frige we have is model KFCS22EVMSO.

Now sure what your layout is, but to make the fridge look 'built-in' you'll still need the room on either side of the fridge for the matching panels. See pics. Your base cabinets end at 24" so there is enough room to allow the fridge hinge and swing of the doors..

This is a freestanding fridge, so it does not affect the value of your house (or can be swapped out for the pictures if you have to sell). That care taken care of, measure carefully. Remember that many full depth fridges still need air circulation in the back, so make sure you're looking at the full footprint numbers, rather than the box depth. Draw it out on the floor with masking tape. If you're not in the space yet, do it where you are, and make tape versions of the nearby cabinets and island too. Fill with boxes. See if walking around the stick-outy fridge bugs you. See if you bump into it a lot. Because that wall is there, no matter what depth fridge you have, it's going to have to stick out so a left-of-picture hinged door can open completely or have a single door opening between you and the working part of the kitchen. This can actually be useful, because you can dump things on the island, but snack raiders and condiment snarfers can be more or less outside of the kitchen while they root around in the fridge. Play around with the possibilities and the tape and boxes, and you'll soon figure out which you want. There are pluses and minuses of each, but it's how you and your family with use it and what will please or annoy you that matters. That's different for everybody.