Sand down the tight spots.

You can scribe over many feet using the front roller of a belt sander only.
Mark what is to thick, sand those areas until it slides under.

Finish carpentry is a different world from framing.

Thanks brickeyee. I had a piece of 1/2" x 3/4" pine there just to close up the gap temporarily, was thinking of nailing it to the studs and then applying trim over it (like the pine). But cousin had a 5 ft piece of 3/4" oak he cut to 5/8", as you see here it is tight in some spots.

{{!gwi}}

Here is the gap each side with the pine strip - I thought that the gap was smaller on the left b/c the pine is a little warped - gap at the countertop at that end too. But it turns out the plugmold is lower at that end.

{{!gwi}}

{{!gwi}}

Here's a new idea - I have 8ft of prefinished molding that came with the cabinets (same as they used to trim out where faces met walls, and back of fridge panel met wall). It's nothing fancy, but it is just the right height to tuck under the receptacle at the tightest spot. Should I nail the pine in to fur out the studs, then use this molding with caulk underneath? The "side splashes" will still be 3/4" oak I have to stain and finish to match, going all the way up to bottom of the upper countertop. I'd have to buy more to trim out above the plugmold (if you think I need to, you really can't see the stud on top unless you're looking at eye level - 34" from floor) since the center of the island is 5ft.

I'm thinking that way, when we want to change the countertop 10-15 years from now, it'll be easier to slide a putty knife all around to break the caulked joint, unscrew the counter from underneath, pull off the pieces he's notching out to run vertically in front of the recessed cabinet, then pull out the countertop. If we're replacing with something of a different thickness then with the countertop off we can pry the sidesplashes and the "backsplash" off from underside without having to remove the plugmold. I'm afraid if he runs one 3/4" deep piece of oak under the plugmold and nails it directly to the studs we'll have a heck of a time getting it off with the cabinet still in place. What do you think?