Actually, since you've already had the heads rebuilt, you'd be better off just rebuilding the 350.
All of the comments from the most knowledgeable guys on this forum have indicated that factory small block heads aren't a good match for a 383, for various reasons.
If you haven't ordered that rotating assembly yet, I'd suggest that you start another thread, and get some advice from the gurus here...
I've seen some 383's for sale with Vortec heads, and I thought that's what I was going to do at first, since I have a good used set of Vortec heads... but the guys here shot down that idea, with detailed reasons why.
So, if you do a 383 short block and put those heads on it, I doubt that you'd end up with something that's any better than just rebuilding the 350.
Another question there is what you're doing for a cam... whatever short block you go with, you'll want a cam and heads that go well with the short block and intended use.
Start a thread with details on your planned usage/desires for the motor, and get some opinions.
Also things like trans, differential/gearing etc. would be good to include.
It sounds to me like your plan will need some changes.
Personally, I'd say if you aren't racing, just cruising, rebuild the 350, and get advice on a cam that makes the most sense for your usage, which I'd assume is cruising and sounding good.
Your situation seems like a 350 with a cam like the Comp L79+ would be all you need.
Just enough duration for a sporty idle, without screwing up anything else.
9-9.5:1 compression would probably be best for a cam like that, but I'll let the gurus give you the best advice on all that.
It sounds like you haven't ordered the rotating assembly yet, so I'd just say STOP, and run this whole thing by this group of experienced guys.
They've saved lots of people from spending money and ending up with a bad experience.
Post your thread Sunday morning, and I'd bet you'll have all the info you need by Monday morning...