Gahhh, mate that film will rot your brain! Every time I see it, it pisses me off immensely - especially as it mentions Montgomery and his 8th Army. Yeah, right.
Well, the film did end with an apology, regarding how action was simplified, synthesized, and in some cases "re-created" (made up

) for either dramatic purposes or to convey the general sense of the events of the battle. They couldn't create a heavy wintery snow storm, so they used what they could. Though even I can't forgive the final tank battle taking place in a
desert! AFAIK, the only desert in Europe is in Poland (the Bledowska Desert).
As to the reference to the 8th Army? Well, it WAS under Monty's command, and since the film was for the entertainment of a general audience, and not a documentary, the film makers were forced to dumb it down quite a bit. How many Joe Schmucks out there would recognize the meaning of "21st, 12th, and 6th Army Groups?" After all, if they had said: "The British Army", then the Canadians would have been pissed, along with veterans of the 9th US Army.
The answer to your question is a simple one - even if he'd kept on schedule he'd have never got beyond the Meuse, as Monty moved XXX Corps there in the early days of the offensive.
This is why I highlighted the schedule and Peiper's rolling a "Yahtzee", meaning that everything ran perfectly for him, and only him. The rest of the German advance being either OTL, or taking advantage from his success by virtue of being in a very nearby sector. Had Peiper been on schedule, he would have been across the Meuse River within 48 hours, before Monty could even have reacted. Throughout the 16th, headquarters was convinced the Ardennes represented mere spoiling attacks. It was nearly the end of the 17th (the end of Peiper's schedule) before Ike finally accepted that he was up against a full scale offensive. To put it mildly, those two days were the worst (professionally) of his and Bradley's careers.
This represents one reason why historians have given so much credit to very small local units, often down to squad levels, for making so many suicidal stands at crossroads that served to slow down the Germans incrementally, until they fell hopelessly behind schedule. In the early days of the battle (during the timeframe of Peiper's schedule) the men in the field were getting no help from headquarters.
Note-I am NOT suggesting for a heartbeat that Peiper had even the remotest chance of "winning" the battle. That is why I limited this to a discussion solely of his own brigade. Namely, just how far does he get before the hammer drops on him, and how does it fall? While OTL and in the film he just runs out of gas, I'm supposing that he and he alone faces minimal resistance, and therefore has minimal fuel consumption in battle (which AIUI is six times what it is just going peacefully from point A to point B).
What I AM suggesting is the possibility that Peiper could cross the Meuse, cruise into Belgian territory west and northwest of the river, and start heading for Antwerp. Or did his orders forbid any such action, requiring him to wait for follow up troops at the river. If not, does he face the specter of the whole of XXX Corps, not to mention any other units Monty chooses to deploy, slamming into his right flank and front?