Hi. I'm the GM of this crazy, messed-up campaign.
First of all, if I may address as many of your questions as possible in one fell swoop:
I am liberally applying the KISS principle to my campaign planning. That is to say: if it makes my head hurt trying to think about it, I don't try to deal with it if I can. Partly because most of the players are a bunch of college students who both watch and read way too much science fiction, and if given the chance they'll spend the entire run arguing out of character about quantum physics, temporal mechanics and why they think they should get extra karma for coming up with stuff that Stephen Hawking made up with in the first place.
[Note: no offense, Thistle. I know you don't do that but you do know who I'm really talking about.
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So to keep the players focused on what's really important, namely the run, I'm making a large use of "Thus Sayeth the GM, Thus Let it be Done." Yeah there are a few rule-lawyer players in the group who don't really like that, but I'm very thankful for the few other more experienced players (*cough*thanksthistle*cough*) who are willing to back me up when I do this.
So as far as the timestream goes, I'm saying that whatever the party does has a direct impact on their future, thus clearing up the whole multiverse dilemna. The time travel device works sort of like a stargate would. It sends the party to a specific place and time, based on calculations made by the scientist NPC.
Tonight was the actual run to stop the New Revolution team. The players started by first hijacking the Delta Force team. They actually had the bright idea of keeping the delta force alive and convincing them that they were all on the same side, and got the Delta force guys to think they were part of some secret NSA team. They entered the missile silo at approximately the same time that I had the future team arrive. The future team was set up so that they wanted to arrive inside the missile silo on the floor just beneath the ground floor where the players came in; thus keeping the suspense up for the players while they went through the military base encountering minimal resistance, until the two groups met up about halfway.
I ruled that the intent of the New Revolution team was to alter the missiles so that the warheads carried a "dirty" nuke (more radiation and fallout) and would detonate in Russia (unlike in the real timeline when the missile is lost before reaching its target.) This would result in world wide condemnation of SAIM, thus cutting off any future support the group might have.
The runners did successfully complete the run. The disabled the arming mechanism for the warhead and strapped some C4 to the missile to ensure that it would be lost before reaching Russia, just to make absolutely sure. Also the runners were very good about cleaning up the bodies of the dead New Revolution team to ensure that no out-of-timeline gear was left behind.
Also for the Delta Force people, the missile was shot off while the runners convinced the D-force team to look for more 'bad guys". The runners then shot off the missile and beat feet out of there. As far as the Delta Force team's involvement, I am going to rule that the team agrees to never talk about what really happened to their superiors. 1) Since they think the runners were some black ops team, they probably don't want to go blabbing to their superiors about a team that "no one is supposed to know about". 2) They probably believe that no one would believe them anyways.
Also on the question of getting money from future knowledge, with the stocks, as long as the runners were wise and not too overboard with what they're trying to do, I'm willing to let them get a little bit of money without losing too much karma. To figure out how much money they get, I planned to look at stock prices from about fifty years ago and look at the big businesses back then and see how they're doing now. (It's the simplest way I could come with for modeling this kind of thing.) I'd average the growth and based on how much the runners bought in the past that's how much they'd have when they return. In exchange I'd probably subract two karma from their total.
The runners really didn't use any of the other schemes, like the availability plan (although the crazy rigger did stash the blackhawk he used in a remote cave somewhere in the wilds of Montana...I'm gonna make him roll his karma pool to see if it's still there waiting for him.)
That's about all I can think about for now. If any of you have any other questions about the details of the run, I'd be glad to post them.