With Mirror Picking...
Pick order goes like this: ABbaabBA (Or whatever equal variant)
Honestly, I feel like this is the easiest way to look at it.
As we can see, if all teams pick the same, then one team gets 18/45 and the other gets 27/36. Assuming all picks were made from best to worst, these are the worst picks you can get in a Strat 2v2.
It is sometimes possible to know which opponent has which intel picks. I have included it in notes on the right.
Possible regardless of which picks you get
17/35 <- One enemy can't have 2+4.
Only possible if you get 1st pick (The A Team in my example)
16/45 <- One enemy can't have 2+3.
17/45 <- One enemy can't have 2+3.
18/25 <- One enemy can't have 3+4 or 6+7.
18/35 <- One enemy can't have 2+4 or 6+7.
18/45 <- One enemy can't have 2+3 or 6+7.
Only possible if you get 2nd pick (The B Team in my example)
17/36 <- One enemy has your 4/5.
26/34 <- Different enemies are in your 1 and 5 picks.
26/35 <- Different enemies are in your 1 and 4 picks.
27/34 <- One enemy has your 5/6.
27/35 <- One enemy has your 4/6.
27/36 <- One enemy has your 4/5.
(Note: In the linked topic, 1368 was said to be possible for a 4-pick 1v1 (Which is like Strat 2v2.) This is impossible; if you go first you cannot get both 6&8, and if you go second you cannot get 8 at all.)