Are you leaving the cabinets in place and just adding the center section flat against the wall?

Reason I ask is because the drawing shows top molding that would not be possible with the over the stove uppers.

Also, the two sides are not the same. There is more area on the left(at the wall) and much less on the range side. That will cause a very unbalanced look.

If you intend to remove the units and fasten them together as a stand alone unit, you will need to add sides---and rework the differences in the side area(as mentioned above). To add sides, plywood would be the better choice. And oak plywood is available at many home improvement stores as well as at lumberyards. The lumberyard ply will be nicer looking, but more expensive.

You might consider replacing the countertop with one made of wood.

Edge banding takes care of concealing the raw plywood edges.

You might think about a couple of different options on making the sides. A/A oak ply is an option as handymac suggests; another is to get A/A oak lumber core, since it generally has a thicker veneer or lay-up some 3/4 TO 1' stock and make the sides out of that. Making it in two pieces so that the upper sits on the base would make it look more like furniture as would replacing the kick with legs. Another option would be to make a solid wood core top for the lower piece and clad it with copper or tin and wrap it around all exposed edges. A solid planked oak top would also be nice. Attach A/C 1/2" oak ply for the back; 1/4" is an option, but 1/2" gives it a little more heft.

Thanks Mac,
This is the wall the new cabinet config will be on:

So once they are in new placement, the filler from the left side is gone. And yes, I am thinking of a butcher block counter top for the new piece. The whole thing will be painted out in a color (yet to be determined!)

DH is thinking plywood for sides also. Will see what he thinks of looking at lumber yard for it. He wants to use two pieces of ply (one on top, one on bottom) and have the sides more open with just the illusion of a connection (a corbel?) We are still wondering what to use for the backing, i.e., beadboard or some other material?

What is edge banding? Is that different from the wood trim we were thinking of using to cover the edges? is it better?

Edge banding is another method used to cover plywood raw edges. Edge banding allows for covering curved edges much more easily than using wood.

The link below is a pretty good quick article.

Here is a link that might be useful: Edge banding

Cabinet is coming along great, can't wait to post pictures!