Congrats on a super strong DL, thats an awesome lift.
You have my analysis basically correcty, but keep in mind this is a method of teaching the lifts based on my belief that there are several positions within the pull that if hit correctly, will ensure a correct pull and will insure that the movement between those positions happens correctly. It is not meant to be an accurate description of what actually happens during the clean or snatch of an Elite lifter.
Hitting the positions, and stopping at the second pull position, which you reach via knee flexion only, then hitting the low hang position, which is reached from the second pull position via hip flexion only, then hitting the floor, which is reached from the low hang position via knee flexion only, and stopping and getting to know each of these positions really well, will do a lot for making things happen correctly on the way up.
When you are first learning, you come up in neccessarily jerky "stages" extending the knees, then extending the hips and dragging the bar up the things, then jumping, there are hesitations at the beginning/end of each stage of the pull. Then you continue to do each rep starting with the lowering of the bar in stages until you can slowly speed up and smooth out the pull on the way up and still hit the correct positions, once you achieve a smooth pull at a decent rate of speed on teh way up, you can stop the lowering of the bar in this manner, and just pull off the floor. Till you become proficient, you will still want to go back to this drill periodically when you feel yourself getting a little "off".
Also, dont worry about your double knee bend. In my experience, when a lifter is taught to do the lifts in this manner, the double knee bend happens naturally without the person even being aware of it 100% of the time. And that is 100% of the time on literally hundreds and hundreds of people, that I have taught to do the lifts, thousands in fact if you count strength seminars in high schools. The double knee bend ALWAYS happens, it has to.
I want to be fair and give credit where credit is due here. I never really thought about or realized the "why" of this till I read what Greg E. had to say concerning the second knee bend. He stated in his book that the powerful hip extension that occurs as the bar is brought into the second pull position causes the knee to bend because the use of the hamstrings in the hip extension movement bends the knee involuntarily. I can see now that my emphasising and exaggerating the period of hip extension without any knee extension happening forces a double knee bend, in fact often forces an exaggerated couble knee bend, and this "teaches" a person to do it, and gets them used to doing it without them ever doing it on purpose.