Given the cost of yanking a head, possibly finding damage, repairing said damage. and assembling the engine.
Just swap in a known good low milage engine and be done with it. Its cheaper and just as easy. its even faster to swap than repair.
You can swap any any LS1 into your vehical up to a 07 classic. 08 was the change over for the 5.3's.
Just for simplicitys sake stay within 01-06 when selecting your 5.3 and everything will work just fine.
Pick up a 5.3 complete pull out from LKQ for aprox 500$, you can get the L33 5.3 ** for alil less than a 6.0, it however is alil harder to find as a complete pullout.
If you can afford it, drop in a 6.0, only thing you need is a Tune (also for the L33). You can get decent mileage complete pullout 6.0's for 900-1500$. just stay with in the same years as you would for a 5.3.
To give ya a idea of the diff between a standard 5.3 vs the 5.3 ** (L33) drive a 08-10 silverado. its got very similar power output.. it will convince you quickly.
The 6.0 however is night and day more powerful than either of the 5.3 versions.
Scoll down 1/4 way to the 4.8-6.0 LS engines and read,
heres link.