First of all I would build the cabinets 24" deep because any deeper is impractical storage. I would build beams of plywood 4 x 4" section and screw to the wall to mount the cabinets to.
I would raise the upper cabinet line to the height of the fridge opening to achieve a consistent horizontal line. If you are concerned with a seam being visible you could add a bead at that horizontal to hide it such as a bead.
You would end up with four face frames applied onsite - upper and lower bank of 3 x 2 cabinets to the right , 2 x 2 cabinets above and left of fridge and two lower cabinets to left.

If you normally use 1.5" stiles uses 3/4" where that come together so all door revels are the same. Hiding joints is not a huge deal most people will never notice.

Even if you need face-frame look, I would build frameless cabinets with oversized doors that protrude beyond edges of the cabinets (not a problem for upper and lower edge, and I think hinges exist for more than full overlay), and then I would put horizontal and vertical beams between cabinets during the installation.
That way, doors would cover seams between cabinets and beams, and the only seams visible would be short lines where vertical beams meet horizontal ones, provided that the horizontal ones run in one piece all the way from left to right.

See the quick sketch on pictures bellow for details (I omitted vertical beams for clarity).

View higher quality, full size image (2167 X 1352)

View higher quality, full size image (2167 X 1352)

Also, I think the design would look nicer is all the upper cabinets have same height and if the fridge is in the middle, if possible.

There are so many ways to do things, what I have done depending on design is to stagger the cabinet depths where they come together. Then wrap your crown molding around the face for a very nice look. Good luck

What D Brown said

Follow Leo’s cabinet layout. It’s always easier to build long units vs tall.

Pack the wall out so you can use standard 24” deep cabs. It will save the customer $2k in plywood. They will barely use the 24” depth.

Two basic options with the face frames. Easy option is to frame each unit then add a little astragal trim piece. The harder option is to temporarily fix the cabinets together in the shop. Apply your face frames so that the upper units frame over laps the lower. You glue, screw or nail The frames on. Do not glue the overlapped joint or butts. Let it dry. Sand it all flat. Disassemble, paint install. If done properly this will look really good. We do this with bookcases all the time. Even beaded face frames.

Thank you all for time spent composing such thought provoking solutions. You guys are amazing, I always get great ideas from this forum.

Leo G. I think your idea for combining cabinets is spot on. Makes sense to me to build them horizontal rather than tall, as you and others have also suggested.

Good idea to raise the line of the second tier to be even with the fridge. I'll try to get the customer to live with the 24" cabinets, we'll see how that goes.

Tom Gardner, I'd love to see a pic. of the bead you you suggest, is it an integral bead routed on the FF, or applied?

Oggie, I think your on to something with the doors covering the seams, I just need to think through it some more.

Adam, I like your idea to let the FFs overlap, I'd love to see some pics. with details of how you do that.

Again, thank you all for your input.

Dave

I think between my idea of long horizontal cabinets and Oggie's overlapping door idea would make the horizontal line between cabinets nearly invisible.

First thing to talk to the customer about is a library ladder rail in there somewhere with a rolling ladder so they can even use the top cabinets. Second is make sure you don't make a full height cabinet, or you may not be able to pivot it up at the install without the corners of the cabinets getting stuck to the ceiling and floor. I usually do a ladder toe kit, so I can have shorter cabinets to tilt up and then slide onto the installed and leveled toe kick. Then add the crown.