not sure why you would want to. You can get an AR in 7.62x39. Rock River Arms makes an AR with a lower made to take AK47 magazines. It is the LAR-47. The lower is made specifically to use the AK47 mag. The AR15s that say they shoot 7.62x39 use a magazine that is straight where it goes in the mag well. This is where jams originate from. AK mags must be curved there entire length.
MGI makes what they call the Hydra system. The lower has interchangeable mag wells on an AR15 type lower receiver. With this set up you can have .45acp Grease gun mags, 9mmP, 7.62x39, 5.56x45 and many more. The extra mag wells are not cheap but much less than dedicated lowers for each caliber.
Sorry, I know I did not answer your question about Saiga conversions, You can have a Saiga in 7.62x39. Is there anything to be gained by making it look like an AK47? I am not meaning to be argumentative, just curious.