Previous owners are notorious (in my experience) for making all kinds of errors (both in concept and installation) as they modify their cars. Sorting them out is torture. You seem to be in that category.
My recommend PROCESS to try and sort things out is to educate yourself on how GM built the car. You'll need the '61 Shop Manual, the 63 Supplement Shop manual, and the 63 Assembly manual at a minimum. If you look you should be able to find all but the Assembly manual on-line somewhere for free. Pay fo the Assembly manual; it's worth it.
Here is a source of some valuable info (1st page is blank, scroll down):
Slow down and FIND OUT WHAT YOU HAVE (what's OEM? What's modified? if modified, to what?) before spending money on crap shoots.
A few examples:
What engine for sure? Where is it's 'power band'? One won't get much response from a wide ratio transmission 1st gear with a 2.73 rear and an engine with a power band in the higher rpm range. Get the 'numbers' and find out what you have.
What heads for sure? 283 heads? That's the only sb from 57. Get the numbers and find out what you have. I'll stop repeating that.
What transmission? Muncie? Borg Warner? Saginaw (didn't come with full size 63 but have seen them installed)?
What rear? 2.73 not available in 63.
The Edelbrock carb (and manifold) should work fine if they are correct for the engine, installed and tuned properly.
What are the tune specs for your modified engine? Timing impacts temps. Don't assume the temp issue is the radiator (don't assume it is NOT either). When does it run hot? At idle? Cruising?
From the pic, it looks like you have a vacuum line from the front of the carb to the power brakes (?). It may be connected to the pcv port, or the manifold vacuum line. Neither is correct. There is a brake vacuum port on the back of the carb for the brakes (I'm guessing you have some variation of the 1400 series carb; it's quite common). What is your pcv configuration?
There is a lot more to discover.
Just trying to be helpful.