360 build ????s

Short of stroking the 360,there is only one way to increase the STATIC compression ratio, and that is to reduce the combustion chamber size.
There are however several ways to do that, none of which are cheap.

There is another way to get some performance, and that is to increase the DYNAMIC compression ratio. And that is where the custom cam comes in, that I earlier mentioned. It'll cost you a few bucks more than an off-the-shelf cam,but if chosen carefully, can make your stocker scoot pretty good.

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You will need a short period,highlift,fast-rate-of-lift cam,specifically designed for the Chrysler .904 lifter, and with an early closing intake valve, to get your Dcr up. You may have to sacrifice some rpm. That means it will be down on high-rpm power. A bit. But it will still make tire-frying, out-of-the-gate torque. I can almost guarantee it will be fun.And you said"Street driving with some fun at the track".
In fact, for street duty,I'll bet you will be swapping those 4.11s out in a hurry.You likely wont get into the 12s with it, but 13s should be pie.