Rope a dope, I like your theory and was thinking along the same lines. Tonight, in the basement, I tied some of my favorite friction hitches simply treating my doubled loop as if it was a singe cord, so everything appears to have twice as many wraps. The key was that because of all the extra wraps and surface area changes, i had to drop the cord diameter to get the desired effect. So instead of tying onto a 9.5mm rope with a 7mm cord, I had to go down to 5mm (i don't have any 6). The bigger diameter 7 and 8 were just too much. And all of these knots held on my pull test in my basement, which uses an intentionally slippery primary rope:
A doubled Distel
A doubled Michoacan... although I had to go with 5 starting wraps instead of the standard 4 to match the distel
A doubled Blakes hitch, which of course has the problem of what to do with the tail.... now a loop, but not integral to the point at hand... it seems to hold.
The only thing I wanted to point out on your photos (which I greatly appreciate you taking the time to post) is with is your last photo where you said that was a michoacan. Although it is very similar to Blakes, unlike blakes, michoacan gets loaded on both ends of the line we tie it with. And so when we tie it with a loop, it needs to take load on all four strands exiting the hitch itself. And so, your knot can't be called a Michoacan, because the load is only on one side of the loop entering the hitch, and 2 strands total. Nevertheless, I tied and tested the knot you showed and it slipped under a good load. But if you are goofing off with it, try this: Given that Blakes and Mich are tied so similarly, think of it as a blakes instead, and when you are finishing it, bring the tail up thru 4 instead of two strands and leave the loop there. That knot seems to hold and binds tighter than the Distel of Mich, but for my application, I need them to really get nice and loose all by themselves when the load is removed... because I am manually tending two of them with one motion. I will do some climbs tomorrow. Thx man.