IMO, Beasley gets the 1st on both of those plays if Weeden gets him the ball.
I would like to have seen more of Escobar, but that doesn't change the fact that Beasley likely would have made the 1st down on those plays.
This is popular opinion and you are very reasonable so I will break this down for you before moving on.
Play 1/Top:
Beasley is 4 yards away from a 1st down running parallel to the line of scrimmage. There are 3 defenders 2 yards beyond the line to gain playing a cloud or bubble coverage meant to NOT allow a 1st down.
1 of the defenders was 1-1 with Dez, the other two were playing the first down marker to be more specific.
But those 2 had eyes on Weeden the ENTIRE time.
Where his eyes went they went. Where his throw went they were closing.
Now take any other completed short play from any game. Or you can use the 2 seconds that tick off from Weeden starting his throw til the ball bouncing harmlessly off Dez.
Now watch that play or any play and watch how much ground NFL players moving full speed cover in 2 seconds. ---About 15 yards
Then tell me they couldn't take the angle to meet Beasley before he secured the catch turned upfield and got 1st down yardage.
I fully realize it looks like Dez is triple-teamed and I realize there was a rub as Sturm details but there is another defender charging up that goes to Dez instead because that's where Weeden's eyes are.
We've run this play a lot this year and Beasley gets first downs on it. But it is a 5 yard play not a 7 or 9 yard play.
The reason Weeden isn't looking at Beasley is because he's not the option in that situation versus that defense.
His route isn't run to gain the necessary yardage.
He's got to either alter the route to go deeper or Weeden has to try and hit the guys who are legit first down targets or take the check down and hope Beasley makes a play beyond the catch.
I respect Sturm a great deal but I actually played college DB.
I watched hundreds of hours of college DB specific film and was cursed out plenty for missed coverages or tackles.
If a college DB didn't make this play they'd be in trouble of getting replaced by a player with better reaction time.
For an NFL player it would flat be embarrassing.
It is certainly POSSIBLE Beasley can turn that into a first down but reality is it is not likely.
He has to keep eyes on the ball and is not going to be lead upfield by the pass.
The play is good for 5 yards every time. 7 is questionable and 9+ means Beasley did something special.
Of the Cowboys receiving options Beasley is the least likely to take a 3 yard pass and turn it into 7+.
He made a great juke to get 12 yards on his 1 catch on the day but reality is Dez, DeMarco, Witten and even TWill have a lot more yards after the catch on the season.
A lot of times popular takes are just wrong.
And as good as Sturm is I'll trust Jaws to review QB tape before a guy who played basketball not football.