So, quickly summarizing:
DE9 female for reference
Code:
5 4 3 2 1
9 8 7 6
7800 joystick:
Code:
R → ← ↓ ↑
L G 5 C
Pins 5 "R" and 9 "L" connect to pin 6 "C" when pressed. Internal resistors pull pins 5 and 9 to pin 8 always.
SMS control pad:
Code:
5 → ← ↓ ↑
2 G H 1
Pins 6 "1" and 9 "2" connect to pin 8 "G" when pressed.
Ok, with that out of the way...
You can't leave the 520Ω resistors in the way when in SMS mode; the pull-ups inside the SMS aren't strong enough to overpower them.
I'm not certain this can be done with only a 2P2T switch. It seems like there's four different things that need to be moved, depending:
[0P0T] Button "2"/"L" can always have one side connected to pin 9
[1P2T] Buttons have a common node that need to be connected to pin 6 or pin 8
[1P2T] Button "1"/"R" needs to be connected to pin 5 or pin 6
[2P1T] Strong-ish pulldowns need to be enabled/disabled