changing wire gauge

If you are only worried about total wiring voltage drop, a small length of undersized wire often makes little difference. But if you are worried about the temperature of the wire, a necked down section will certainly get hotter than the larger wire, and with high enough current may melt its insulation or even melt the wire, acting as a fuse. You should calculate both effects to make sure you will not have problems with either voltage drop or peak temperature.

how much "headroom" is there in the rules about wire thickness?

has some rules. 6 gauge wire will run 101 amps in a chassis wiring configuration. 8 gauge will do 73 amps and 10 gauge can do 55. When does it really start redlining? The description says its a "conservative rating".

These ratings are based on some packing factor. I don't know what that is without a bit of digging, but a wire can carry a lot more current without overheating when it is suspended in air than it can when it is tightly bundled with lots of other wires that are also carrying the same current density (amperes per cross sectional area). More conservative ratings apply when the wire is wound tightly around a hot magnetic core. The rating also implies some maximum temperature based on the insulation temperature rating, so vinyl coated wire will have a lower maximum ampacity than, say, teflon coated wire, all other things being equal. You might also have to worry about other materials against the wire that either melt, degrade or catch fire easily.

None of this addresses the question of acceptable voltage drop, which is a system question, not strictly a wire question.

The rule of thumb is, if you don't know how to calculate temperature rise and voltage drop, you use conservative wire sizing rules to cover your ass.