The scenario is Pieper's Race.How do you know there are lots of Allied reinforcements heading for Stavelot and Trois Points/
From the history. Maybe that's cheating. Historically Peiper was cut off when the Allies attacked Stavelot coming down behind him from the Spa direction. He ended up running out of fuel at La Glieze (after retreating from Stoumont), had to abandon the tanks and armoured cars and make his way back on foot at night. There's still one of his Tigers parked up in La Glieze today. If you get further than Stoumont then you've beat him. There was a famous fuel dump on the Stavelot-Spa Road that Peiper missed because he didn't go up that way.
But also the map. I suppose those bridges have to be key Allied objectives, because there's not much else between there and your exit points. I would definitely defend them as you move forward - not with a whole Bn, but with enough to hold them until you can get reserves in to help (if you keep a reserve), otherwise you may end up out of fuel too. As you know already (you probably know all this already, sorry) anything that happened historically is likely to happen in game when you're playing the historical scenarios. Historically, Trois Points was blown in Piepers face, I think. If you shell the defenders with any kind of arty before and as you're moving up your advance panzers then you might avoid this fate.
Also, to be honest (and in which case, sorry again, as it means I should have done a spoiler warning, perhaps - so SPOILER WARNING!) I've played this scenario many times. You might not even try to go nth of the river, of course. It's possible to use the crossings further sth and go up the western edge of the map. Historically you would then be straying quite close to an area that was being desperately reinforced by allied airborne troops, and you might end up running into them. I've never got better than a draw as Pieper, so my tactical advice is probably worth very little. But I try to play them historically, mostly, not doing things that Pieper wouldn't have done (like, due to very poor recon, and the constant danger from the air, he would never have tried to go up the far west of the map), in which case, I suppose, I did alright to get a bit further than La Glieze. Good luck!
Just remembered, there's a picture of Dave standing next to the La Glieze Tiger somewhere over in the Matrix forums!
This book (and the second volume) are great if you can get them for less than the absurd amazon price.....
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You could probably do a luxury battlefield tour for a month from anywhere in the world for that price!