Bleeding it is not bad.
Do you know where it is leaking? The ends are replaceable, that may be cheaper than getting a new radiator. The low coolant sensor likes to play games, if you know you have coolant, leave it be for a few heat cycles. Do not go drilling holes in the thermo, and it is also a good idea to get a new 160 or 180 thermo, remember to get a LT1 specific one. It is NOT a SBC thermo.
As for the bleeding... fill the system with the bleeders open, when they begin to drip coolant, shut em, put on rad cap and start car. Let it heat up and then crack the bleeders with a rag under them. Basically it, do that a few times and you will be set.
Best site for good info.
http://shbox.com/1/4th_gen_tech2.html#cooling