My church does enforce the standard of women having their heads covered during The Lord's Day, but that's the extent of it.//
Wait... just curious, does your church require that even when those women are not in church (ie. after church on the Lord's Day?
The problem with the whole veiling 24/7 when out of the house thing is that it carries heavy legalistic connotations, which run afoul of most of the 1st table of the Decalogue. Furthermore, attempting to introduce any practice with even the slightest flavor of Islamic influence should be met with forceful resistance, and I'd definitely refuse the sacraments to someone going in that direction, in part because I wouldn't want knowingly allow them to drink judgment upon themselves while in a backslidden state.
OK fair enough. Though seriously... honestly would your church give communion to anyone who isn't part of your particular congregation anyway?
P.S. - I know this isn't OPC dude, I'm simply stating my position on the matter and recounting some of my own encounters on this topic. This is actually one of the points where the Reformed Steelite wing makes a clear break with others claiming Covenanter status, we're not in the business of adding stuff onto established standards without a full church review, which is naturally difficult in the church's current state.
In what way do covenanters currently do this?