They do get crossed, look again.
The inside signal lead of the of the POT go to the outside trace of the other POT, so they are crossed, just no wiring gets crossed, if it's done right. The way your diagram was just had the lines crossed, but if ya look at it ya have the inside lead going to the opposite sides inside lead, which would have resulted in it being SP (if it were on the signal lines instead of the power lines) but also inverted on both axis as the signal lines wouldn't have been rewired properly.
The way you planned to do it (pulling the sticks is how you mentioned it in your PM, 'no trace cutting' it was) needs no trace cutting, you just run the pin from one stick over to the trace of the other, the right hand side pins/trace are the signal ones, but both pins on the right hand side need to be cut as to not make any contact with the traces as they are connected internally on the button. It's pretty much the same as with the POT leads really if you plan to do it by pulling the entire sticks.
Either that or you cut the traces and cross them after the fact and since you have 6 of them I'd need to know the board version of every one to show ya what traces needs to be cut where as well as what TP spots to rewire them to as that can differ from boar version to board version as well and I'm sorry but to be quite frank I'm not the one getting paid to do those things and if you are I'd try earning that money a little bit for a change. There's more than enough info around here to get it done, pretty much all of it in this thread really, so ya have a few options there...
You can use a multimeter and magnifying glass to find that stuff out much faster for yourself or...
Pull the stick and trace it completely out so ya know what goes where or...
Use the pics in the SixAxis controller versions thread to help out with all that or...
Wait until I get around to doing up proper tutorials for all of the different versions of boards that Sony keeps tossing out, which is going to be awhile, if ever, since playing tutorial keep up with them isn't exactly my idea of how to have a good time. I honestly wouldn't be surprised if ya had a board version I haven't seen yet either as many of them as I've run across so far.