what flywheel

HaH!!
If you are running THAT on the street you can run anything for a flywheel!
Seriously.
But I would still run the beast.

And here's why; in about 500 miles or less, you will figure out that 12.13 is ridiculously low for the street. And 4.10s or 3.91s are gonna find there way in there, and then that big cam is gonna want some flywheel.heehee. So you can save yourself the headache of pulling the lighter flywheel right from the get go! I ran your numbers and get a Dcr of about 7.9 at 156psi. So yeah with 3.91s you'll feel the hole. 4.10s not so much; but the heavy fw would provide relief with those,during initial engagement. This is why I run the deep low in my box.
But, on the off chance that the 4.56s are in for the long haul,you can run anything. You have enough starter gear for aluminum. Flip a coin,as to aluminum or middle-of-the-road steel.. You don't need heavy.
As to power;IMO I doubt you will ever see the difference. Yeah it will make a difference at the track. But a streeter has about a 65 mph speed limit. That is usually a one gear run. Not so much for you.With 4.56s it maths out to the top of second gear.And the biggest problem for a streeter is hooking. Zero to 60 is somewhere between 5 and 6 seconds for us. So even if your engine reved 2% faster.............would you see it in the time slip?
I'm more interested in the vast majority of city driving which involves a start from zero mph, than the minuscule percent of the time I actually need to win a sprint. I only have a 367 with maybe a tad over 400hp. I am geared for 65 mph =6900rpm in first-od (with a GearVendor). 295s spin the whole way. I don't care one tiny bit if my engine could make a teensey bit more average horsepower, cuz I can't make use of what I already have. And I like it this way. I'm not in it to win races. I'm in it to have fun,and try to suppress the urge to giggle.Grown men should not giggle, right. heehee....
Yeah so,if you got your eye on a lighter fw, just go for it!

But I tell you what; if you have not yet driven this combo with the heavy flywheel, and you have one,I highly recommend that you do.Then you can make an informed decision based on real-world experience.