First, the results. I had some good success with improving Governance early, but I'm fairly convinced that the way to win this game is to prevent Islamist Governments in a few key locations, one of them being Pakistan. If you can survive with an 8 card hand, that means you can get move two troops to three more countries other than Saudi and the Gulf. For me, that meant Pakistan, then Sudan (after Somalia went Islamist), then Jordan. By the start of the final deck, I had gained and lost Sudan as a Good government, and while the Gulf and Saudi went Good fairly early (with a certain amount of back and forth), it was Jordan that was the fourth Good country.
Making things harder were an Islamist Lebanon. Go HAMAS! Not really. The biggest problem with Lebanon is that it's right next to the Shengen countries in Europe, and so lots of travel there while there were cells present. I managed to get the Ethiopians to take out the Somali Islamists, but shortly thereafter Sudan went Islamist. Fortunately, I had pulled my troops out so no Prestige hit.
At the third deck, I got really lucky on the second hand. I had managed to turn Pakistan to Good Governance with some lucky WoI rolls (and good Prestige and a Good Gulf States nearby), and then I got the magic combo. I had had Kemalist Republic in the first hand, but no chance to really use it. Turkey was a Poor Ally, so I could have used it. However, in the second hand I ended up pulling Oil Price Spike, which let me take it back. Not only that, it gave me 11 Good Resources instead of 9, so I could go after an obvious country like Turkey for the win instead of Iraq (which was Adversary and Poor).
And, of course, I rolled the six on the WoI table to get Turkey to Good, winning with 13 Good Resources.
My impression is that, like most solitaire games, you need to use good tactics, good responses to bad combinations of events, and a long view. However, as I've said on BGG, Lady Luck is a stone cold bitch and Irony is sitting on her shoulder. There's no other way to have it in a solitaire game, if there isn't a luck element then you just have a puzzle, and what fun is that?
If you are going to play the Soft game, here are a few things I've found that seem to make a big difference:
1) Prestige is key to a win. Since you can't knock the Jihadists out by killing all of their cells, you have go to for a Good Governance win, that or getting a lot of countries to Fair as well. I think that latter method is a sucker bet, too many chances for the Islamists to Jihad and Plot your ass in too many places, and Radicalization makes extra cell placement and travel far too easy. That means you need to make WoI rolls, and you can't do that with your Prestige in the toilet.
2) So how do you get Prestige up? Disrupting cells in countries where you have 2+ troops, so early on you want to get countries to become Allies so you can place them there. As I said above, you can have up to 5 countries "corseted" like this unless you want to drop down to 7 cards per turn. Of course, if you need a little extra time, that can be worthwhile if you can get Funding down as well. Remember, however, that FATA will show up regularly, so if you are in Pakistan (and you should be in Pakistan if you're going to have an Islamist country next door) try to get the Indo-Pakistani Talks played too if at all possible. Troops are also handy if the country goes Adversary, which Saudi did with me thanks to Al-Jazeera. You need to keep those countries as "clean" as possible, because even Good countries tend to have successful Jihads from time to time.
3) Going hand in hand with keeping Prestige high is to disrupt Funding. An 8 card hand is worthwhile if the Jihadists have the same or smaller hand size, so do what you can to drop this down. Be aware that there are a lot of cards that bump this back up, but if you have the chance to drop Funding down to a 7 card hand, it will pay off in the long run.
4) Go for the Domino effect as much as possible. Adjacency is a big deal in this game when it comes to Travel for the Jihadists, so having a cluster of Good countries makes it harder for them to be infiltrated en masse. Don't get too confident, however - Radicalization will drop a cell in the middle of the pack right after you get your troops out, and that doesn't help anyone.
5) Understand which cards are not going to be usable when you aren't Hard or in Regime Change (and being in Regime Change while you're soft will make it hard to keep those troops in those Good countries). An Islamist country isn't necessarily a bad thing, and in fact I managed to win with three of them in effect at once. However, there are a lot of cards that require a Regime Change marker on the board, and they aren't all US cards, which means more Jihadist cards that you don't have to play the event to use.
6) Strive for constancy of Posture. Don't be afraid to Reassess if you can after a Posture shift. Soft is going to cause problems, but no more than Hard will, and you have a statistically better chance of GWOT not being a factor as well as countering the -1 Prestige ding you get at the end of the turn. Plus, no GWOT dings for WoI rolls too. I think that sticking with one Posture throughout *most* games is a good idea, although there are definitely times when a temporary shift can give you the benefit of an Event or two if you get lucky with the card draw. Still, WoI is the path to victory in the solitaire game, and you can't win if you have a -3 GWOT nerf against you.
I've played a lot of Labyrinth solitaire recently, and have enjoyed it quite a bit. Having the ability to play as the US using different strategies is very appealing, and adding in the US nerfs to make it harder will be interesting. I definitely think that the game will go where the cards take you (and, to a smaller extent, the dice), but in the end the game has great narrative features and works well on VASSAL (especially if you have a couple of monitors, as I do). Hopefully the suggestions I give above will help you take on the Jihadists while staying Soft.