airtren, let's see if I can be more rigorous without getting into details. That is to say, I'll wave my hands a bit. Hopefully somebody with numbers will then step in.
What really needs to be accounted for is the energy imparted by the engines and the energy removed by drag. In that calculation you use the difference of squares rather than square of differences. Then you add in the energy from the continued thrust Et and subtract the energy lost in drag Ed. In level flight. At FL350 these two figures were roughly balanced. So somebody who knows the engine thrust at FL350 can figure a "static" value for Et and Ed. That allows a modified Ed for the duration of the climb to be estimated. Then we can really figure out of something was holding that plane down or not.
(I played on the back of an envelope and have a suspicion that the plane was indeed in a wind with a downward component of some sort. But it's such a swag I'm not going to publish it. I was pulling numbers out of the air and Wikipoodle.)