A small-base die will not reach any further down the case than a standard die, so going to a smaller die is not your solution.
The usual Pacific T-slot shellholder is standard at .125" deep. You cannot size any farther in conventional equipment. BUT, there is also the die mouth to consider, the entry taper or radius varies brand to brand. Dillon dies have a wide mouth for smooth progressive operation. Lee has a smaller mouth and sizes a bit farther down, the EGW/Lee a bit farther still. The CFC die leaves rub marks to within .200-.220" of the head.
And push-thorugh dies, which can reach all the way down to the web of the case, don't work very well on tapered cases, so I don't think anyone makes one for 9mm.
As I said, there has been some work using a Makarov CFC die body as the push through for the Bulge Buster on 9mm P. Some say it helps, some not.
Brass shot in an unsupported chamber has been displaced well beyond specification and there are no readily available tools to "fix" it, so I recommend brass fired in an unsupported chamber be disposed of.
There ARE "readily available tools." There are push through Bulge Buster types from Lee, Redding, and Case Master, $30 to $6000 depending on your volume. The Case Pro roll sizer is popular with USPSA shooters to iron out their racegun empties, as shown by Slamfire.
Or they use .38 TJ brass, which is .38 Super with a huge extractor groove so that the sizing die can reach the entire sidewall.
I would be wary of fully sizing .40 cases out of Glocks et al, but the 9mm does not worry me. But 9mms are generally well managed by U die and/or CFC, and are cheap, so I don't see the point in individual processing.