I finally figured it out. The file I posted was something I was messing around with while I was at work today, so I wasn't thinking thing through clearly. I was trying to map my IPAC button numbers to the MAME default keys, instead of mapping MAME button numbers to my IPAC controls. So, in other words- completely backwards.
All it took was a looking at the in game tab menu for a NeoGeo game to figure it out.
So, for those that may have the same problem, here's the fixed file:
<mameconfig version="10">
<system name="neogeo">
<!-- neogeo input configuration file -->
<input>
<port type="P1_BUTTON1">
<newseq type="standard">KEYCODE_LCONTROL OR KEYCODE_C</newseq>
</port>
<port type="P1_BUTTON2">
<newseq type="standard">KEYCODE_LALT OR KEYCODE_LSHIFT</newseq>
</port>
<port type="P1_BUTTON3">
<newseq type="standard">KEYCODE_SPACE OR KEYCODE_Z</newseq>
</port>
<port type="P1_BUTTON4">
<newseq type="standard">KEYCODE_X</newseq>
</port>
<port type="P2_BUTTON1">
<newseq type="standard">KEYCODE_A OR KEYCODE_J</newseq>
</port>
<port type="P2_BUTTON2">
<newseq type="standard">KEYCODE_S OR KEYCODE_W</newseq>
</port>
<port type="P2_BUTTON3">
<newseq type="standard">KEYCODE_Q OR KEYCODE_I</newseq>
</port>
<port type="P2_BUTTON4">
<newseq type="standard">KEYCODE_K</newseq>
</port>
</input>
</system>
</mameconfig>