well you have the same alt my car takes.
that bracket indeed does work, as i had a 270a ad244 on my car using it.
you've gotta shave down a bit on your alt mount for it, but its fairly easily done.
however what we can do with the stock case will have more idle output than a 350 will, by about 10-20 amps or so. Not to mention they're a more efficient alt. We can do a hairpin conversion on the stock case which will do around 300a peak but 220-230 @ idle. I'll be putting one on my car in the next couple weeks, as we just finished development on them. The only downside is you'll lose that rear mount. Its nothing to worry about, just letting you know.
edit: i didn't go with a 350 on my car as the crank pulley belt wrap is horrible, i just didn't trust the lack of belt wrap there to try to turn a 350. i believe your car is a 3800 series 2 mine is a series 3 so it may be different.