Has anyone ever tried playing this scenario with the Lannisters placing the Strategy Tokens and knowing their locations instead of the Starks? My girlfriend and I played it the way it was written in the Scenario Book but it seemed plausible to do it the other way as well. 

I've never done this (or even played any scenario more than once so far). Given that I lost that one as Stark, I think it might be a bit unbalanced when Lannister places the hidden tokens. Given your question, I would assume that Stark won an overwhelming victory when you played it, and you are looking to balance it more in the Lannisters favor? I would be interested to read a battle report, in that case.

Here is ours: http://lannister4live.tumblr.com/post/11312446189/battle-of-the-green-fork
(inserting clickable links does not work using Chrome on Linux - this Forums software could use some work).

 It does seem like a lot of these scenarios are balanced more towards Stark than Lannister, particularly as the Stark heroes are just so ridiculously powerful. Robb's King in the North variant is impossible to catch, Greatjon (in Greatjon form) is a beast in combat, and Karstark is also impossible to kill. Addam Marbrand is good, but not when facing other commanders and the Mountain is very powerful, but incredibly slow. It could just be that I'm a lot better at this game than my girlfriend, but I feel Stark may have the advantage in a number of the core scenarios. 

 Also after reading that battle report you posted, I was wondering if you agree that both regular forces and commanders can take markers in the Green Fork scenario? My interpretation of the rules was that any Stark unit could take a marker, but a Commander could only take one, and if he was killed after taking it it was removed from play and the Stark player lost a point. 

TheHil said:

Yes, that's the way I read it, too. That's also a part of the reason I lost - I only had a commander units left, so no way to pick up further tokens.

About the balance: We have played the first 13 scenarios so far, and the score is Lannister 7, Stark 6. I think we're about equal in skill. So far, I found them well-balanced, and am looking forward to play them again. All our battle reports (written by my opponent) are here: http://lannister4live.tumblr.com/
(and also on boardgamegeek).

I forgot to add something: I recommend playing with the optional rules. We used "coordinated attacks" and "any card to order 1 unit" for all scenarios, but only started to use the "reduced strength units" and "withdrawals" with scenario 11.

Reduced strength units make those invincible commanders (red robb, greatjon, gregor) somewhat less effective.

 Yeah, those rules seemed intriguing. For the sake of confusion, I'm probably going to play through all the core scenarios once, and then replay them with the optional rules as Lannister. I'm ordering Wardens of the West this week, so I'll have a couple new scenarios and those extra gambit card rules.