I have been seeing some posts here about the "Ps2 remote" lately and assumed they all referred to the IR remote, not the "controller," which is the term I am more used to hearing. If it is the controller you are talking about, then I think there may be a few small errors in the pinout you listed above. For example, L1 and L2 are not present, and there shouldn't be two extra pins with no functions. There are many different revisions of these controllers, so the pinouts on the connectors may vary, but here are my results:
1: L2
2: L1
3: Up
4: Left
5: Down
6: Right
7: Select
8: Analog
9: Start
10: GND : Digital Buttons (Start, Select, Analog on/off)
11: GND : Analog Buttons (Other Buttons)
12: GND : Mysterious Ground (through a resistor?)
13: Square
14: X
15: Circle
16: Triangle
17: R1
18: R2
Also, using the left analog stick for the face buttons is going to be awkward because it will be the reverse of how the PSP is normally played (face buttons controlled with right hand). To use one of the joysticks for controlling the face buttons you will need to desolder it and make some simple modifications to the potentiometers, TimmyDX shows how to do this is his
video tutorial.