The reds derived from the madder root are much "earthier" - more of a brick-red shade. Think of the common British redcoat's uniform compared to the scarlet of an officer's uniform, and you'll know what I mean.
The tartans that are listed as being in "ancient" colors generally have that orange-ish, brick-red shade you're looking for.

This guy also makes "period" little kilts:

http://www.angusharveykiltmaker.com/18thckilts.html