The way I have it set up right now is that the pedals are mapped to the analog, and the inc and dec each have a value of None, so it looks like it is set up properly I believe.
Sounds good to me. Hmm...
The pedals register as Joy 1 Accelerator and Joy 1 Brake. No mention of any axis when I input them into the controls, but as stated before this seems to work fine with all my other driving games. Since there are no axis, it looks like I can't map half or full axis, correct?
Nah, mame just adds the plus or minus to whatever the name that directx tells mame the axis is called. (You can do a quick check by mapping a pedal to any digital input temporally.) With what you're saying your setup is, I don't think you'd want the half axis anyway, but I tested and mame has it working again.
FWIW, to switch between full and half axes, start off like normal: tab, select either intel general or this game, go to the analog port of an analog input, enter, press your pedal, wait until mame registers it, press enter again, press pedal again, wait until mame registers the plus half. If you want the minus half, press enter again, press pedal, and wait. (repeating a third time returns it to normal full axis.)
The times you want the half axes are when you have combined pedals (or combined analog triggers on gamepads, or using a normal analog stick's up for gas & down for brake) on mame's pedal inputs, or in the quarterback/baseball "spring stick" games.
In you case, with split pedals & mame's pedals input type, you'd want full axes anyway.
It's starting to look more like I'm out of luck since everything appears to be configured properly, unless there is an area where I can do some configuration that I'm not aware of. I read over the two links you posted and was already pretty familiar with the content in that section of the FAQ.
Just checking.

It does look like it's a game specific issue.