What would you do?

Sounds like the following combo will suit you:
-340 w/ 4" crank
-new pistons to run with the stroker, probably about 9-9.5:1 CR max with iron heads.
-Aluminum intake, high(er)-rise/dual-plane, optimally an air-gap.
-Probably around a 750-800CFM carb, depending on the cam/heads. If you're going to drive it on the street, I'd avoid the double-pumpers.
-Clean up the J-heads and install larger valves if they're not already in there.
-Dougs/TTI headers, unless you want to scrape.

When you start looking at cams, make sure you match the cam to the motor and what you're trying to do. Call Comp Cams or Hughes and get a good idea of what kind of lift/duration you need to drive 100 miles to the track, race, and then drive home.

The 3.23s are going to hold you off the line, so don't get too wild with the cam. You will need some serious torque, but the stroker motor should help with that.

You should be able to hit your goal, but the wrong combination of parts could easily hold you back.

Good luck!