I think so far I’ve had the most success so far with Jemison as in identity, maybe in the world, having had tournament success with three different builds (this isn’t saying much, since not many people play Jemison, as it’s fun but not amazing). There’s a couple ways to play it. One is as a FA/Rush deck, kind of as @analogBrad is describing. The other is as a more Glaciery deck with some FA tools to help you get there.
First, no matter which way you’re going, you really want 3 Oberth Protocols. They let Jemison do what it wants to do; sacrifice agendas to score bigger agendas. When you sacrifice an agenda and have to just use the advancements for some ICE, it kinda sucks; agendas are much better.
Second, I’d spend some of that left-over 12 influence. Spending all your influence is a great idea no matter what, but I’d say it goes double for Weyland, since a lot of their cards are kinda garbage.
I’m also in agreance that the Space ICE (Asteroid, Nebula, and Orion) are probably too slow to play. They’re really only playable if you hit one with a Priority, but since you have 7 of them in your deck, the time will come where you have to put one on a central, and then it’s way, way to slow and expensive to have to advance it into something that makes any sense to rez.
Here’s a list I’ve been having some success with that’s similar to yours. I’ll discuss it afterwords. It actually includes a lot of what we’re talking about here.
Jemison Astronautics: Sacrifice. Audacity. Success. (Daedalus Complex)
Code Gate (6)
15 influence spent (max 15, available 0)
20 agenda points (between 20 and 21)
49 cards (min 45)
Cards up to Down the White Nile
The first thing you’ll notice is that I’m playing a Vanity. This is something I like in Priority Construction Jemison because it gives me something to do with the advancement tokens. Namely, use Red Planet Couriers to score it out of hand with Biotic. This is fairly easy to do if you are able to score an Atlas with 2 counters off of an Oberth protocol (click one, install Atlas onto an unrezzed Oberth, rezzing it by saccing a 1-pointer, advancing Atlas twice; Click 2, advance Atlas, which is then advanced again by Oberth; Click 3, advance again and score). This usually allows you to go off and score Vanity once you see one of the 3 pieces, or at least finish advancing things so that you can very soon. If you don’t like it, just replace it, Oaktown, and Pop-up, and replace them with 2 Global Foods and maybe an Meru Mati.
Another thing I’ve done is put a lot more into the deck that can go into the remote. With Priority Construction, one of the best advantages of it is being able to quickly create a fairly scary remote, and it’s best to take advantage of that by shoving things into it for the runner to run on (or that they can’t run on). I usually run 2x Shipment From Tennin, but I’m using that influence to try out Calibration Testing instead. It’s another thing to go in the remote, which I like a lot, and doesn’t have the restriction about the runner not running, but it’s also much more expensive, and takes a turn to set up. So far I think I like it, but as I said, still testing. NGO Front is completely busted and one of the best cards in the deck, since you can make the runner run and spend their money, and then go ahead and take 8 credits at the same time. I’m also a sucker for Sapper, which gives R&D a little more protection by allowing you to potentially trash programs if they’re unlucky enough to access it. It’s also great vs MK Ultra for Anarchs, costing 3 to break.
Anyhow, that’s my take on the deck. Either way, I’d find a way to spend that influence, get another Oberth in there, and maybe get some better ICE. If you have any questions or comments, don’t be afraid to ask!