If my intent is to do the program, now what?
Have you read the blue book?
I just ordered it.
For what it's worth, those deadlifts do not look like the deadlifts of someone who is not physically capable of pulling 335.
The answer to this light deadlift is to push it up aggressively. Take 10 pound jumps for a bit. A light deadlift for a squat isn't in an of itself a problem: it will come out on the squat, so just let that happen as it does and introduce the requisite programming changes (light squat day etc al). The problem here is that your deadlift is not what it could be at your strength level, not that you are uniquely bad at deadlifting. Applying the programming principles in the books will cause you to arrive at a more appropriate ratio.
For the record, I know I am capable of pulling 335. My all time 1 RM is 385 (which I know is still not great). A better way to describe my feeling that day was that if I forced out those 5 reps, it was more likely that I re-injure myself than walk out of the gym healthy.
Backed off to 275 to practice not jerking the bar.
275 - YouTube
You are not going to injure yourself pulling 335 off the floor.
This is your problem: you are being precious about the deadlift. If you want to increase your deadlift, you will have to pick up weights you think you might not be able to pick up. The deadlift is not going to injure you. There is no magic technique fix that is going to make heavy weights feel less heavy. Worrying about lagging on a lift you have *never authentically missed a rep on* is a completely backwards approach.