Yeah, the Atman and 3xTyson seem like a missed opportunity for your influence. Even the Special Orders don't seem particularly helpful... spending 13 of your 15 influence on that mix is pretty rough.
Mondo is right on with the Knights and Datasuckers. The rest of the breakers (either specific or Overmind) are a toss-up. Pick what you like, but I do like the idea of Deep Red, a couple Mem Strips, and an Overmind.
I don't mind the idea of running a resource-heavy deck out of Anarch, but there's a lot of tools that come with that (most for free) that can solve the problems you've found in this deck. Something like 3x"Off Campus Apartment" and 3x"Paige Piper" are going to help you rip through that deck much quicker, both thinning and drawing. If you need to go even faster, Duggar's will get you to an e3 guaranteed. Likewise, running all these resources, you really don't have any excuse not to find some room for either Career Fairs or Hostage/Supplier. Those two cards could save you half the install cost of this entire deck.
I'd look towards starting with an influence package that looks something like:
3x e3 (obvious)
3x Clone Chip (recursion of Parasites/Datasuckers/Knight)
3x Career Fair (econ boost)
As for econ, I think you've got more than enough in there (with Gambles/Armitage/Daily/Liberated/Kati/Symetrical), but most of that is pretty slow and can take a lot of tempo to install and get money from. If you're looking to speed up, I'd drop the Kati's and Symetrical and trade them for some draw (3x"Ive Had Worse", 3x"Inject").
Basically, a lot of the answers you're looking for are already in faction, and I think the rest of the influence kind of picks itself just based off the programs that need to be recurred and the amount of resources in the deck.