Personally I would love to remove the OAIs but there isn’t a viable econ card to replace it. Beanstalk isn’t good enough, and I’m already using both Hedge and Restructure. Given the influence is going to be used for the deck’s gimmick, I don’t think using influence on say Sweeps Week is a good idea.
I do wonder whether a deck that dedicated to murder wouldn’t be better out of GRNDL. I mean, I understand Blue Sun’s ability is powerful for making sure you never waste credits defending your centrals, and in theory you can score out of a remote if the meat damage doesn’t make itself available.
Do you think an ice suite with just Hadrians, Changeling, Wendigo, Hive, Caduceus and a smattering of Tollbooth/Wall of Thorns is taxing enough? If Curtain Wall isn’t necessary, then that might be the way to go. It would reduce a lot of early game awkward draws and make the deck less reliant on the huge OAI bounce play - assuming of course, that you can find the econ elsewhere somehow?
Edit: Just as an aside, I’ve tested the Mushin/Grid/Punitive list on Octgn just to see if it actually works.
So far, 3 flatline wins (1 Reina, 1 Kate, 1 Andy with MO!) and 1 win against Reina by scoring out (without Grid, just remote). So maybe the Punitives are snatching games by surprise when they shouldn’t be, but it looks like the list doesn’t completely fail 
Having said that, some games were pretty rough early. I am struggling for money more than I thought I would be. Because of this, I haven’t actually used Off the Grid once yet.
I did initially doubt the 3 Archived Memories but it seems like they are necessary. They reinforce the Punitive kill as well as giving me extra OAI (if I’m lucky) or Hedge if I’m really struggling. Hive has been as amazing as expected.
I almost think Curtain Wall is overkill at this point, although the Andy flatline only happened because the runner spent all his money breaking Curtain Wall on HQ. I also did manage to PriReq a Curtain Wall twice, so there’s that.
I think I would be happy to drop Curtain Wall and OAI if there is a reasonable econ option in faction. I guess I could try Amazon Industrial Zone again in this shell for a recurring money source, but having it trashed before I can use it twice for the net gain sucks.