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Solve with either Petrus or ZZ up to this point, then try making the pairs with the last D edge in place. In the U layer, they should be adjacent to each other and there should be a "T" of unsolved pieces (if that makes any sense). I can upload a picture if you are still confused.

So if I understand correctly, you want something like this:
Scramble: L' R F' B' R L' F2 B' L D2 L F R2 L B' D2 U2 R B2 L' U' B' D2 F L

EOline: U R' F' L2 U' B D
First block: R2 U2 R U L U' L U R' U L2
Pairs: R2 U R2 U R2 U2 R2 U R2 U2 R
Solve block+orient LL: U2 R U2 R' U2 R' U2 R
PLL: L U L' y R2 u' R U R' U R' u R2 U2
50 HTM (I think, might have mis-counted)
 
Roux/screw variation:

Cubeshape
Left block
Right block
CP+ setting up the last two bottom edges opposite of each other
M2
EPLL

Sometimes you might want to insert the last two edges before CP if they are already opposite.

I have used this as my main method pretty much from the beginning and I average sub-20 with it. It may not be as fast as vandenbergh, but with only 15 algs (may vary depending on how you count) it is a pretty good alternative. I also think I can get down to about 15 with this.

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Roux/screw variation:

Cubeshape
Left block
Right block
CP+ setting up the last two bottom edges opposite of each other
M2
EPLL

Sometimes you might want to insert the last two edges before CP if they are already opposite.

I have used this as my main method pretty much from the beginning and I average sub-20 with it. It may not be as fast as vandenbergh, but with only 15 algs (may vary depending on how you count) it is a pretty good alternative. I also think I can get down to about 15 with this.

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Looks cool, how many cases would it be if you did CP+ bottom 2 edges in one go instead of doing CP+M2 setup?
 
Looks cool, how many cases would it be if you did CP+ bottom 2 edges in one go instead of doing CP+M2 setup?
18 algs if I'm correct, but I have no idea how to generate sq1 algs.
But only 18 if you do a 0,6 before some algs, otherwise almost twice as much.

I can do M2 in .3 anyway, so I don't really bother.

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So if I understand correctly, you want something like this:
Scramble: L' R F' B' R L' F2 B' L D2 L F R2 L B' D2 U2 R B2 L' U' B' D2 F L

EOline: U R' F' L2 U' B D
First block: R2 U2 R U L U' L U R' U L2
Pairs: R2 U R2 U R2 U2 R2 U R2 U2 R
Solve block+orient LL: U2 R U2 R' U2 R' U2 R
PLL: L U L' y R2 u' R U R' U R' u R2 U2
50 HTM (I think, might have mis-counted)

No, but this isn't a bad idea either.
After the pairs are made, put them both on the left instead of the front like you have it in this solve.
First we insert the back one wile orienting the corners (this will help recog I think) then insert the front one while doing PLL.
28 Corner Orintation cases, haven't done the math for PLL yet.
 
So this isn't really a method, just an idea for CFOP users--couldn't it potentially be good to do a sort of "half EO cross," where you only orient the edges needed to build the F2L while doing your cross? Not sure if this idea's been explored or not, but maybe it could be helpful in particular scrambles where partial EO is really easy to incorporate into the cross solve?
 
So this isn't really a method, just an idea for CFOP users--couldn't it potentially be good to do a sort of "half EO cross," where you only orient the edges needed to build the F2L while doing your cross? Not sure if this idea's been explored or not, but maybe it could be helpful in particular scrambles where partial EO is really easy to incorporate into the cross solve?

ZZ-TOP is very similar (only difference is line instead of cross) and probably a bit faster.
 
Well, certainly not something to be consistently used as a method, but maybe just another way to take advantage of lucky scrambles? Like, if you see you can really easily orient all your F2L edges while solving cross, you could do it and potentially remove rotations while still keeping other benefits of CFOP (structured, relatively easy lookahead, mostly 2gen burst tps). Kind of like how with good scrambles you can try and go for x crosses.
 
Well, certainly not something to be consistently used as a method, but maybe just another way to take advantage of lucky scrambles? Like, if you see you can really easily orient all your F2L edges while solving cross, you could do it and potentially remove rotations while still keeping other benefits of CFOP (structured, relatively easy lookahead, mostly 2gen burst tps). Kind of like how with good scrambles you can try and go for x crosses.

Sounds like you may want to check out edge control during the whole F2L. Feliks has a video on his channel.
 
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