I think I agree, 350 is probably a good number, depending on your definition of "reliable".
However...
have you ever been to a race school, and talked to the race instructors about the cars they run? In my experience, it is almost always something with a cage, harnesses, all the suspension mods, sticky tires, and a STOCK engine. Most of the guys I know that are really into track time don't mod their engines much at all. Maybe very basic stuff, and perhaps some cooling/oiling mods, but power usually isn't something they are after. The most reliable version of an LSJ is the 205hp one that came out of the GM factory.
I wouldn't worry about some basic bolt ons, those should be fine. Maybe a slightly smaller pulley (don't over do it), headers, air filters, stuff like that. But if you're messing with balance shafts and cams and such, it probably won't be as reliable as it was when it rolled off the showroom, even if it still holds together.