Thanks. 
Re the pot rack, yes, with a large butcher block below and an eat-in dining area on the other side of it. This pic shows about half the space.
I wanted to show the perspective of the staggered-height cabinets.
Looks exactly like my fridge. I hate the side-by-side design (narrow and deep ) personally.
Are the cabinets attached to the glass doored cabinet? If not, I would just raise up the cabinets over the fridge, reattach to wall, and not worry about it not being flush on the bottom.
Looking at the picture, I’m wondering how much height you could cut off that particular cabinet without it ‘looking funny’ (and losing utility as storage).
Because your cabinet tops don’t currently all line up, I’m wondering if raising the cabinet or cutting it down a bit and raising it a bit (cutting it down involves removing it temporarily anyway) might save storage and preserve aesthetics.
This is a nothing-burger for a cabinet shop if there’s one near you that could spare the time, and they’ll be able to retain proportion by – if necessary – relocating the handle and/or the lower hinges.
Also, if the face frame extends lower than the bottom shelf … it might get you an inch toward your goal without really hurting aesthetics, particularly since putting a fridge under there tends to obscure sight lines – at least to the very bottom of that cabinet.
Good luck !
You can say that again. I’m so tired of practically having to climb into the fridge to find the stuff I want at the back.
The cabinets aren’t attached to the glass doored cabinet. Yours is by far the easiest solution. But as @DavidNRockies points out, preserving the aesthetics is important to me, too.
This is what makes the most sense to me. I appreciate your reassurance that such a project is a doddle for a cabinet shop. Removing the cabinet is within my own abilities, and we do have a few cabinet makers in the area who might be willing to make some extra money in their spare time to help out an old lady. Especially if she brings cookies.
This… is also brilliant. Although if fridges of the future grow even taller, then the doors would have to be redone again, wouldn’t they?
Realistically I’ll probably only be here for another 10 years, although who knows? Either way, I wouldn’t want to leave a mess for the next owner of the property.
I knew you guys would come through with great ideas. Thank you!
If an easy option is to just completely remove the short double-width cabinet directly above the fridge, I don’t think it would look strange - I honestly think the aesthetics of your kitchen would be improved. You then have good visual symmetry between the high & low cabinets to the left of the fridge and the high & low cabinets to the right, “framing” the fridge & door opening. You could display something attractive and visually interesting in the space on top of the fridge.
In the grand scheme of leaving turds in the punch bowl for the next owner … don’t worry that this one rates
If you would rather have a smaller gap today, and you get there by either cutting down the cabinet or raising its height on the wall, then the next buyer need only raise it another inch – probably not an issue.
At some point, the top of the cabinet could even end up close enough to the ceiling that a bit of crown molding adds visual interest (or the cabinet goes away, to @Riemann 's point).
But if you can get close enough by just cutting down a face frame … that’s probably the way I’d go … unless you truly liked the look of the cabinet sitting higher on the wall.
That would be by far and away the easiest solution.
I’ll have a chance to test out the aesthetics when I remove the cabinet, because as others have pointed out, that thing has got to come out one way or the other when I decide on a new fridge. I can leave it as you suggest for a few days to see if I could get used to it. I sort of hate to lose the shelf space it provides for the things currently atop the cabinet, but that’s a comparatively minor annoyance.
Remove cabinet. Make top portion of cabinet into shelf. I think it would look better actually.
Believe it or not, I had actually worked out this option on my own. 
So yes, I don’t have to lose the shelf space.
Ponders…ponders…I choose to believe it!
Purely aesthetically, I think leaving the top portion as a shelf is visually less attractive. Too many straight lines at too many different heights. I prefer removing it completely, and putting something interesting in the space.
I was imagining it at the same height.
Looking at your picture I’m wondering if the new fridges really are any taller than your existing fridge.
It seems like the cabinetry is sized to fit the rear of the fridge but the doors stick up higher. Is it possible that new fridges are the same dimensions as yours behind the doors and you are just looking at the dimensions to the top of the doors?
You know, that’s an astute observation. Before I go willy-nilly tearing out a cabinet, easiest thing in the world to head over to the outlets where I’m thinking of buying the new fridge with a measuring tape to be sure.
Some of the fridges I’ve looked at do distinguish the height of the unit from the height of the doors, but most don’t. If the solution is this easy, I’ll be delighted!
It won’t be perfect, but I would seriously consider just raising the cabinet over the fridge 4" like you were thinking. It is the easiest and most efficient. I’m guessing that cabinet has 4 screws into studs in the walls and maybe 2 to the cabinet next to it. It should be a very easy job as it is a very small cabinet.
To be honest, it wouldn’t be the easiest solution, but my personal solution would be to raise not only the shelf over the fridge but also the one to its left so they both aligned with the taller shelves even farther to the left…Being me, I might also do that on the other side of the doorway too so everything had the same height.
LOL, you know, my friend, I was thinking that in the time I’ve spent dithering about a solution, you’d have already had that thing yanked off the wall and repositioned. I’m right, aren’t I?
I’d be willing to go to that much trouble, too, except then nothing would be aligned at the bottoms.
More and more I’m coming around to the idea of simply eliminated the cabinet. It’s not that much cabinet space and there’s another whole bank of cabinets that aren’t shown on the left of the photo, plus another bunch further to the right.
I realized I misspoke earlier when I said the photo shows half the kitchen. It shows only about a third of it.
This is what I did. My cabinetry was done in the 80’s. When I bought the place, a fridge was already in place. But, it was not only too small for my cookery/freezing needs, but it smelled like cigarette smoke, as did everything else. So I bought new, without measuring. My bad. A pair of friends came to my rescue and took down the cabinet, and shaved the bottom lip off and rehung it. It fits, I still have a cabinet, though rather hard to reach.
As a warning though, The wood on that cabinet was at least 35 years old. In that time, even soft woods can become hard. Per the couple, it was a pain in the butt to cut.
Pull the cabinets out, put in your new fridge and then shave the cabinet doors down so they will fit over the fridge and hide the hole. I’d cut off the bottom of the doors because I’m short and can’t see the top of the fridge, I certainly can’t see the bottom of the over the fridge cabinets we have.