So I've noticed that AI-controlled civilizations seem to begin turn 1 with about half of a warrior already built (haven't checked to see if this is the case on higher difficulties when they start w/ archery). I was wondering if you can eliminate this little bonus, and if so how.

The easiest way to do so would be to alter the GlobalDefines file. Just change <Define>
<DefineName>INITIAL_AI_CITY_PRODUCTION</DefineName>
<iDefineIntVal>10</iDefineIntVal>
</Define> to a number of your choice (so probably to 0).