Lets clear a few things up, OK
Vortec is part of the LS family. It's a 5.3L truck motor.
Most people, when referring to an LS are talking about and LS1, LS2, LS3 etc. This is true across the industry.
I will not swear to it, but I do not think anyone is making an adapter to mate the 60 series split case to a T56.
If you are looking for a manual, your best bet is an NV4500. This is my opinion, as is all of this.
If you think you can do a swap for under $5K, count on working on it a lot after the swap is done. I have done many swaps and I can tell you that the 5.3L pull out (used motor) swaps I do in my shop are far more than that in parts alone. Sure, you can get a junk motor for a grand or less and sure you can use the radiator that is in the truck now, and the old fuel lines and you can bolt a cheap fuel pump to the frame. You can even re wire the harness yourself. And sure, you'll be fixing something most every weekend instead of driving it.