Are you sure you don't do an x'? I might just be confusing myself. But here is how I do my A(a) perm. You put the dual corners so they are permuted correctly. Do a U. Then do a y' x' and this should put the currently correctly permuted corner in the upper left. I use the same perm that you do. You should notice when you do the U that all 4 edges should be permuted correctly as well. Doing A(b) you do a U' instead of a U, still put the correctly permuted corner in the upper left (this time it should be just an x') and then do the A perm
in reverse (R2 D2 R' U R D2 R' U R'). You'll notice when you do the U' that the edges are also permuted correctly.
Also please note that if you do A(a) when it calls for A(b) you'll be left with an H perm, and vice versa. So basically if you see the edges oppositely permuted, U2 and do the other of what you were about to do
I find that the easiest way to recognize the A perms are just by the edges alone. If they are all permuted correctly, or permuted opposite, then I know what needs to be done. Not to mention the "headlights" really help out, but my main focus is to look at those edges.
Really I've noticed that no matter what PLL I'm doing, if I'm doing it 2LPLL style or just a single PLL perm I happen to know (I know about 14 of them, started out with 7 but quickly learned mirrors just to help myself out), I pay attention to the edges. Say you're doing an A perm for corners, paying attention to the edges lets me know what U perm to do. Since the U perms I use happen to be identical except the direction you turn U the first time, it makes it very easy for recognition. I really need to learn the faster U perms (only using R and U), the greatness about them is that like the A perm, Ua is Ub in reverse. Anyway, back to the edges. When I'm doing a 2LPLL that calls for the E perm, watch those edges again, it'll let you know which U perm to do. Not to mention if you use badmephisto's E Perm you can easily set it up so that the solved side will end up in your left hand letting you do my U perm and already looking ahead at which side you need to turn U. This sounds really confusing, I think.
Here are my U perms:
Ua - B2 U' M' U2 M U' B2
Ub - B2 U M' U2 M U B2
But I hold the cube differently, with the solved side in my left hand. So the B2 turns into R2, and M turns into S (I believe). But if you can see here (either on your cube or visualize) the U or U' goes towards the cubie that's oppositely permuted to where it needs to go. Again it's kind of hard to describe without just showing you. Anyway, this U perm allows me to set up quite easily after doing badmephisto's E Perm (which seems to be pretty popular: x' R U' R' D R U R' d2 R U R' D R U' R'). or the A perms I use. With the A perms, I just leave the R face just turned twice, then go right into U S' U2 S U' R2, or U' S' U2 S U R2. It saves you from doing R2 back to back at the end of the corner permutation then starting it for edge permutation. And with the E perm, instead of ending it at R', I just do an R and then either U/U' S' U2 S U/U' R2, instead of pulling R back down with R', then doing R2 etc.
Again, back to those edges! You can very quickly see the case when you will have a Z perm following the A or E perm you are performing. Depending on which Z perm you use, you can again be quickly set up into the Z perm right after your A/E perm.
I think what lacks to be mentioned a lot is that you don't really have to learn as many algs for beginners method as believed. When I first learned how to solve, I didn't learn E, Z, or H perms. I just did A twice (for the corners) or U twice (for the edges).
