I'd keep it very limited.
Tool wise I'd stick with quality tools and blades, I'm a big lover of O1 so probably similar to what he had. I also take 240, 800, 1200 and 6000 Japanese water stones to get a superb edge on everything. I think I'd keep a good Leatherman on me as well as they are so useful.
Modern fabrics for clothing and tarp/ poncho would be a must for me, light and more effective and warmer though it is hard to beat a good old wool blanket (I love a good bit of canvas and leather, no kydex for me).
I'd also take my homemade catapult with me with modern rubber (though no idea what it was like back then) for hunting small game.
The main addition for me would be I'd have some kind of solar charger and good battery to charge up with it for a few modern gadgets, and a good DSLR camera with modern lenses to take photos, 70-300 would be a must, I'd also like a simple laptop with Lightroom and the internet (most likely routed off a mobile phone so I could also use some useful apps available and read books on it at night too) to post photos and get info or post info on how to do stuff, I'd probably do a blog aswell. I'd bet if someone on here did do it the thread would be massive.
I think that would be about it, as the whole point is getting away from it all.