There was a recent post on how to make the same sling but with an easier method. The simplest way? Buy some.

If you have a dropdead date for needing your slings I bet a few people could send you something.

Also Humdinger

http://slinging.org/forum/YaBB.pl?num=1172017416/2370

Hey, I have never made a King Tut sling in my life.  I have barely browsed through the tutorial.  What I do is making braided slings with knitted pouches which may look like they could be Tut slings. 
Almost the real stuff, just looks better, faster to make and use way less material
Feel free to ask me about them.

The loom is the easy way, believe me. Make the loom about 12" each way to give yourself plenty of room to work. Make one now with whatever you have available, you will learn a lot with your first attempt that you can use for your second.

Don't be discouraged when the first few passes look like a spider on meth, after a few more passes it sobers up and looks respectable.

Start now and aim for your third or fourth as being the perfect one.

Good luck and post pics

No arguing with a master. I do what David says too.

don't you have cotton or some other smooth yarn ? Wool may tangle way easierly (how do you say this ? ) and since you will have a lot of yardage to tighten the weave, it may result on hell on earth...

For some reason cotton never cooperated when I tried making it into a Tut sling. It always stretched in all the wrong ways, never stayed in place, distorted the warp no matter what I did, stuff like that. Nylon was a bit similar. They weren't the most forgiving in the learning curve. Jute however, cooperated VERY well. I recommend learning with jute until you get it down, then use whatever you like after you manage to pump a good one out first. (Jute's also cheap, so it's better than burning away some-300' of that expensive linen warp with each attempt. )