I had considered this route a while back and did some research into getting the materials.
Here are the technical drawings for the military specification:


(Sorry for the low resolution; this is the best I could find.)
The hardest part is finding 2.25" milspec OD webbing. The closest I’ve found is this:
http://www.lowyusa.com/wb8c-r-resin
It has that same herringbone pattern with a seam down the middle, but it’s wholesale and special order, meaning you’d need to buy a LOT of it.
The same company sells some of the hardware:
http://www.lowyusa.com/tb4042
http://www.lowyusa.com/bk205
But again, same caveat with the special order/wholesale deal, and the spring quick releases on LC-1 hardware had little metal stop tabs on them.
I’ve not been able to find the metal loops and plastic tooth part for the quick release on the left strap anywhere.
1" OD nylon webbing (for the top and bottom attachments to the strap) is much easier to come by and available all over the place.
One thing I had considered was buying some of the cheap LC-1 style mil-spec straps (the kind that blend LC-2 pads and strap styling with LC-1 quick releases). I have a pair and the metal hardware is nearly identical to real LC-1’s:

(Original LC-1 on the left, Repro on the right)
There’s also more than enough of the 2.25" webbing once you rip the seams and unfold it, as it’s doubled up LC-2 style in places, whereas LC-1 only requires a single layer of it over the pads.
The color of these repro straps is more brown than green, but nylon takes dye fairly well (use lots of vinegar), so it shouldn’t be too hard to green them up a bit.
You’d just need to reshape it, sew new 1" webbing on (what’s on these straps is far too short) in the right configuration, reuse the old hardware, and sew on new nylon pads.
I think I paid $10 for these straps, so that might be an avenue of some interest to you.
This will be a really cool project if you get it off the ground!