Steve, I have only done this with melamine-faced particle-board, which is the standard for kitchen cabinet carcasses over here. To me the clipped corner is a bit like Love Story - never having to say you're sorry. I unashamedly copied a commercial unit, as those guys had already sorted out the issues for ease of production.
1. The oblique filler piece was much wider than yours. If one butts the two back pieces at 90 degrees, that additional space is largely wasted - a lot of users cannot comfortably reach into the corner - I can't. I imagine that there is a carousel in the cabinet, and think of clearing the carousel with the filler piece - the rest is wasted space to me.
2. The filler piece was bevelled at 45 degrees along each long edge. Easier to do than beveling the larger end pieces. Placed as Charles said, on the inside, with the bevels facing to the back. If the end pieces are at a true 90 degree orientation to each other, two clean joint lines, no need to worry about the length of the hypotenuse compared to the thickness of the panels. In your case, you will be able to glue the bevels to the plywood faces - not possible with melamine.
3. The thing to pay attention to, is that the filler piece needs to extend the thickness of the top and bottom at the back - that way it can be fixed to those components, adding to rigidity and antiracking. One can attach a small triangular piece to close off the bottom of the cabinet into the corner - the top is less critical, unless you will be placing small stuff on the top - been there.
4. In my case, the vertical components were fixed to the top and bottom by dowels for alignment, and knock-down fittings to pull everything together - not fine furniture standards, I know, but 20 years later, not a smidgen of movement.
I don't know how you will make or attach the frame - in my case, it did not matter on some of the cabinets, because they had complementary doors or bi-fold doors. Some others were even cruder, but because of the Euro-style overlapping doors, it was not a glaring faux-pas. The door will have to open to about 160 degrees, if you will be using Euro hinges, otherwise access is restricted.