I think you might have a slightly skewed version of what is, and isn't, overpowered, if you think 16 dice for a combat test is overpowered. Shadowrunners are not the equivalent of first-level characters. They have been doing their jobs for awhile - they may not be the best of the best, but they can start out as pros who have the potential to break into the ranks of upper-echelon runners eventually.
One thing to remember about dice pools is that Shadowrun has a lot of situational modifiers. Sure, they have 16 dice unwounded, facing a stationary target a point blank range - but what if it is raining, there is glare from street lights, the shooter is wounded, and the target is at medium range, and moving?
The availability restriction is, frankly, way over the top. They can't even get simple things like smartlinks or wired reflexes: 1 with those limits. You might as well say "Don't bother playing anything but an awakened character or a technomancer." An availablity restriction to 8 would fit a low-powered 300 point game (although I would restrict Magic/Resonance to 3, to keep it relatively even). A 450 point game should have the full normal availability, though.
If your players truly aren't that bright, then let them make powerful characters - they will need that edge, simply to survive by the skin of their teeth (if at all). Shadowrun is a very tactical game. Ganger punks who spread out and use cover (as well as some other elementary tactics) can ruin a much more powerful PC's day. But at least if bad things happen to their characters, they won't be able to blame you - because if you restrict them after the fact, every bad decision they make will magically be your fault. It won't be "Gee, I guess a running charge at four guards with submachine guns was a bad idea." Instead, it will be "Damnit, if you had let me get some decent armor and that dermal plating, I could have soaked that damage."