I would use the 350 block and build a 383. It is not than much more expensive and the power increase would be significant while still retaining good street manners:

Eagle or SCAT rotating assemby with flat top or dished pistons (depending on your heads) for $1200-1300. If you have to bore your block, you will have to get new pistons anyway, and you should by all means put aftermarket rod bolts in your rods and have them resized; and if you have to have the crank turned--well you can see how the new assembly makes sense in the long run.

You don't say whether your 350 block is a roller block or not, and what kind of heads you are planning to run. Without knowing this, it is not possible to make any recommendations.