I wouldn't "convert" the barrel - it may digest 9x23 fine. That .001" of bore difference falls well within the range of manufacturer variation. 9X23 very closely resembles hot loaded .38 Super in pressure, velocity and gross dimensions.
If you want to go whole hog, just replace the barrel with a Barsto. The breech face is a tad wide for a 9mm case head, but this won't be a problem. The mags will be 100%.
The only other consideration would be increased recoil over whatever Tangfoglio might have spec'd (given the wide variation in .38 Super load power). The best solution might be to use an increased power mainspring, which helps slow the initial slide movement, rather than screwing with the recoil spring. A buffer might be appropriate as well.
Again, I'd try some hot .38s, then some 9x23 in the factory barrel first, just to see how well it shoots. If the accuracy is good and the cases aren't deformed or showing any signs of high pressure, that could be "good enough". Otherwise, a fitted barrel and maybe a mainspring should make for a complete project.
All that being said, these are inexpensive guns that work well for 9mm through 10mm. But there are reports that indicate that the 10mms, in particular, show wear after not too many rounds. I don't know what hot .38s or 9x23 are going to do wear-wise over the long haul. It would be a shame if you spent much energy on the project and the gun wore out in 20,000 rounds.
