Okay, here's my final post on what exactly I ended up with and a few things I learned in case anybody else needs the info.
Before anything else I want to give thanks to TheNasty for the basis of all this and his wiring diagram as a place for me to start. I hope he doesn't mind but I used his drawing as a basis to mock up the rest of the drawings I present here. (I just wanted to give credit to the original drawing.)
5 Volt Counter
First, I want to address the 5 volt counter. Definitely nothing against TheNasty, I couldn't have done this without his diagram as a starting place, but there are a couple things about his diagram for the 5 V counter I discovered.
I'm 99.999% sure the diodes are not needed with TheNasty's diagram. By putting the counter on the ground side you're putting it on the side that's normally common anyway even if the counter wasn't there, so the diodes aren't needed to protect against all coins firing when only one input is closed. (I.e., the coin switches themselves prevent the other inputs from firing.) The diodes certainly don't hurt anything by being there though, they just don't seem necessary.
Second, while this is certainly the most simple way to wire a 5 volt counter it may or may not work depending on the counter. In my tests trying to use a 5 V relay in place of the 5 V counter (which would then close the relay switch for the 12 V counter), which electrically should be essentially the same (both an electromagnetic coil), I couldn't pull enough current from the I-Pac inputs to fire the relay coil. The inputs still triggered on the I-Pac but the relay wouldn't fire. So it's reasonable to guess that some, perhaps not all or maybe not even most, but at least some, counters will be the same way. To solve that, I found an alternate wiring diagram in an old thread that somebody had drawn by hand. I've cleaned it up using TheNasty's diagram as a basis. It's the first diagram attached to this message. Here, we pull 5 V directly from the PC power supply through the counter so we're sure to have enough current to drive the coil. Also, here the diodes are definitely needed because we're combining the input side of the switches.
In summary of the 5 volt counter if that is what you have, I'd say definitely try TheNasty's method first since it is much easier, and doesn't require a separate line direct from 5 V, but if that doesn't work then try this alternate wiring method.
12 Volt Counter
Now, on to the 12 volt counter. This uses the alternate 5 V counter wiring method as a basis, and essentially just inserts the transistor into it. The second diagram attached here is the wiring I ended up with. I did try to build this off of TheNasty's original method initially (putting the resistor on the ground side of the switches) but again, I couldn't draw enough current through the transistor to get the counter to fire that way.
Two quick notes reagarding this that you might want to modify in your own circuit.
Note that there are two sets of diodes in my circuit. The set at the top coming out of the transistor serve the same purpose as in my alternate 5 V diagram, to keep all inputs from firing when only one switch is closed. These diodes are necessary. The 2nd set of diodes coming out of the I-Pac inputs are to protect from any 12 volts from going back into the I-Pac. That would be bad. Technically, these diodes from the I-Pac inputs shouldn't be needed since theoretically any time the 12 V flows it should be going directly to ground through the switches and can't go back into the I-Pac, but I didn't want to take any chances. They certainly don't hurt to be there and I thought only about $2.00 in diodes to protect my $65 I-Pac was worth it.
Second, the 100 ohm resistor into the base of the transistor worked fine, until I tried to hook up the coin door lights to the PC power supply as well. At that point the counter would no longer fire. The lights worked fine and the I-Pac inputs still triggered but the counter wouldn't fire. If you need to run any other devices off your 12 V from the PC power supply, you should be able to reduce that resistor until it does work (try a 47 ohm, if that doesn't work try a 10 ohm, if that doesn't work, try eliminiating the resistor entirely). In my case I just happen to have a completely separate external power supply that I decided to run the lights off of.
Last, attached are front and back pictures of how I took this circuit and actually implemented it on a small PC board (back view is flipped left to right from the front if you're trying to figure out how the wiring on the back corresponds to the components on the front). The inputs from the I-Pac connect to the bottom. The top terminals go to the coin switches, the wires that would normally go directly to the I-Pac. On the right side (in the front view), 5 V comes in directly from the PC power supply on the bottom terminal, 12 V to the 2nd to bottom terminal. The top two terminals on the rights are the out to (2nd from top terminal) and return from (very top terminal) the counter. Essentially the middle two terminals on the right side are just shorted together so the 12 V comes in and then goes right back out to the counter. This just made it easier to run wires so I could run both the 5 V and 12 V lines from the PC to this board instead of 5 V coming to this board and 12 V going to the counter in a completely different part of the cabinet. And then similarly coming back from the counter, only having one wire returning from the counter to the board. Probably uses more wire this way but is more "discrete" (for lack of a better word) in having each component with it's own wires. Oh, I do still basically have to run the main PC Power supply ground directly to the I-Pac ground though. I used a terminal "barrier" strip to connect to the I-Pac ground connections to give me more connections to ground.
Hopefully this is all a bit clearer than mud, but if anybody has any questions I'll do my best to answer them.