Converting an Amiga Mouse to a trackball or Rotary Knob

I have a few games which require either a trackball or a rotary knob to play (for example, CABAL, and Arkanoid). I do not own a trackball or rotary knob and don't really want to buy one either (although I may pick up a trackball in the future if the price is right). I decided instead to convert an old Amiga mouse I had laying around into an input device compatible with these games' requirements. Fortunately, the signals from a trackball and rotary knob are the same. The difference lies only in the number of axies used. The conversion is quite simple, actually. The Amiga mouse outputs TTL signals with the exact data these games require! Only problem is, the games require CMOS signal levels. To convert from one to the other, add a 4.7K pullup resistor (pullup is the name of its' job, it's not a special kind of resistor or anything), and attach it to +5V on the other side. Only the Vertical and Horizontal data wires need pullups. The rest of the wires simply need passed through to the appropriate location in the arcade machine. 
The pin numbers in brackets are the pins of the DB9 (9-pin plug):

Mouse                                  Arcade Machine

Middle Button       (5)  (No Connect)
Left Mouse Button   (6)  >----------> Button 1
+5V                 (7)  <----------< +5V at Power Supply
GND                 (8)  <----------< GND at Power Supply
Right Mouse Button  (9)  >----------> Button 2


The next 4 signals may need swapped-around depending on the game.
If the axis are swapped, exchange these pins on the mouse: 
swap 1 and 2 then swap 3 and 4.  The axis have now been exchanged.
If the direction is backwards, swap 1 and 3, *OR* swap 2 and 4.
(depending on which axis which is moving backwards)

                             ^ +5V at Power Supply (or PIN(7) below)
                             |
                             \
                             / 4.7K Resistor
                             \
                             /
                             |
Vertical Pulse      (1)  >---+------> Up   

                              ^ +5V at Power Supply (or PIN(7) below)
                              |
                              \
                              / 4.7K Resistor
                              \
                              /
                              |
Vertical Quadrant   (3)  >----+-----> Down

                               ^ +5V at Power Supply (or PIN(7) below)
                               |
                               \
                               / 4.7K Resistor
                               \
                               /
                               |
Horizontal Pulse    (2)  >-----+----> Left

                                ^ +5V at Power Supply (or PIN(7) below)
                                |
                                \
                                / 4.7K Resistor
                                \
                                /
                                |
Horizontal Quadrant (4)  >------+---> Right

This new controller must REPLACE the existing controller 
in your cabinet, they cannot exist simultaneously.
I have added a DB15 inside the arcade machine which I 
can plug in this device, or the standard joystick/buttons.
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