I've used the factory reproduction harnesses from M&H (
www.wiringharness.com) which were absolutely plug and play - taped, all connectors attached, proper length for factory placement, etc. With the interior out, it took less than 4 hours to rewire the car. You can also get them with the modern blade style fuses.
I've also used the AAW Classic Update harness. Plan on spending about half of what a full M&H harness will cost you, and several days getting it installed, as there are many options, you have to install virtually all the connectors other than the bulkhead fuseblock, and wrap it if that's what you want.
Most LS1 harnesses have only four connections to the car's harness. The AAW Classic Update harness probably adapts better to an LS1 (mostly because it's unwrapped and un-terminated), although it also wouldn't be too hard with the M&H.