With a '69 340 you have to keep in mind that pistons patterned after the stockers will be around .018" proud of the deck. This makes closed chamber heads a little entertaining, not only because of the compression ratio you get from the small chambers but also because of the valve/piston clearance.
I built up a '68 340 that's about to go into my Duster, I've got KB243's in mine, which are in fact .018" over the deck. I run a set of 308 heads (open chamber) on it that have been ported to get the flow I wanted. With 65cc heads, a .039" gasket and the 243's over the deck .018" I ended up at 9.8:1. (The 243's being over the deck mean there's some extra calculations on the piston volume side, I got my numbers with some help from KB tech).
You definitely want to pick your heads first on this one. Keep in mind that if you do go closed chamber, you may need to spend some extra cash getting a piston that will work for you. For a 350 hp build, I would suggest just staying with the stock heads and having a little work done to them- 2.02/1.60 valves if they aren't already, maybe a little clean up/smoothing work on the ports and a good valve job. That will be more than enough for 350 hp, and you'll be able to use off the shelf KB pistons and not worry too much about valve clearance.
Here's a link to some 360 build ups. Gives a decent idea of where you need to be with a 340, figure on a little less HP and torque based on a few less cubes and shorter stroke. But on the builds that are close to 1 hp per cube, you'll be in the ballpark for 350 hp. Notice that on the builds that are less than 400 hp most of the heads are basically stock, just the 2.02/1.60 valves and a little clean up work.
http://www.mopar1.us/dyno.html