You have options, and the "correct" answer is not necessarily the ZL1, don't listen to the top trim snob crowd.
The first very safe option is definitely getting a ZL1 (6th gen of course) and never touching it. You can have powertrain warranty and the best Camaro trim GM ever made. The problem with that, however, is that you apparently have a strong enough desire for "moar powa' babeh" with a 2SS 1LE that you are exploring forced induction, and a stock ZL1 at 540-570 rwhp is unlikely to satisfy that need, you will eventually want more.
Option two is a what you described, getting a reasonably easy to install supercharger kit, PD or centrifugal, slap it on, then get a proper tune from an experienced tuner. As King said, you will be making the same 540-570 rwhp but running on the ragged edge without more octane (ethanol or methanol), and longevity is unlikely with that setup.
Option three, you can obtain roughly the same power level with NA upgrades (fueling, big cam, heads, LT headers, intake, tune), without running any boost, which, at least as much I understand it, means you can keep your LT1 bottom end and still stay safe.
Option four, the one I took, is the most expensive (we're talking ZL1 money or slightly more), but it gives you everything in the end: have a competent shop 1) upgrade your fuel system plus add flex fueling, 2) strengthen the bottom end of your LT1, and 3) add a cam, heads (maybe), intake, LT headers and/or forced induction for much more than stock ZL1 power. My car is rock solid, the fuel system isn't struggling, WOT injector pulse width is at a safe 5.3-5.4 ms, target and actual lambda at 0.82-0.83. And, I can use ethanol to run the engine cooler and make extra power. The car made 735rwhp on the dyno and is very consistent on the street. In terms of power, I have made it to the point where I don't want more, no decent streetable tires can hold significantly more than what I have without big compromises, and the car is already enough of a freaking monster when pushed hard.
In the end, it's your money and your car. Listen to King(LT1) and others here who have a boatload of experience, and make your best move. Good luck
