I think if you start with a Std Base Corner cabinet, then play with the multiple settings, you will be able to achieve your goal.
Once you select the corner as your seed, notice the blue arrow under Cabinet Edit. This will give you the options for setting any of the base dimensions. Be sure to go to Construction Settings and set the Corner Settings Tab to Angled Front.
I tried starting w a corner cabinet and change the settings you indicated. I had a lot of trouble with this approach, as it kept telling me it would result in an unstable cabinet and would not make the changes.
I tried your suggestion again, and had a little better luck with it...certainly a lot closer to what I am after. I think the difference was the construction settings which I had not previously changed.