Here I go again, "against the grain"... We get "flack" all the time for building "baby big blocks". I like 396. It's a good, solid basis. I shares the rod/stroke ratio with 427, and revs just as nicely.
I believe the heads you have with the 325 HP version, have fairly good sized oval intake ports, at least "better" than most mid-70s and later oval ports. The "closed" chamber makes things a LITTLE tougher, but not a big deal. Icon makes a nice replacement piston that's lighter than the Speed Pro, and you can still machine the dome to "fit". Both the Icon and Speed Pro are readily available and up to the task.
We install the 2.190/1.88" valves in the oval port heads all the time. A little "blending" in the bowls is all that's really needed, and they can "feed" a 396 well over 7,000.
We built one last year for a "show/go" Camaro ('70 SS396). With the Muncie, 3.73s and "street slicks", it goes 11.70s. 93 octane, reasonable idle, 13" of vacuum, "all done" at 6,500. Comp Xtreme Energy solid flat tappet, 236/242 @ .050, old fashioned Torker intake, AED 750 HO carb. Woo Hooo!!
So, yes, 396 can be a very potent street engine. And no, you don't need the monster money parts to do it.
BTW: All 366s, 396s and 427s used the 6223 crankshaft. Good forging. I don't believe you need a 4-bolt until power exceeds 600 HP or RPM exceeds 7,500. Then, installing splayed-bolt caps to your existing block would be infinitely more desirable than trying to find a 375 or 425 HP block...