"That aside though, I think Cecily's point (if I may be so bold) is that the new covenant clarified and enhanced tithing/charitable giving the same way the new covenant did with the rest of the law, in that the standard is actually higher than originally thought."
I agree. Jesus Christ upped the ante on keeping the Law of Moses in Matthew 5 ("You have heard it said, but I say to you ...."). It makes you realize just how much you need the atonement He made for our sins. Regarding the tithes in Israel, I have read that tithes were never money. They were always agricultural products. One example is your referenced verse Deuteronomy 14:24.
Right, turns out tithes were never money (and I don't think I ever realized that til today), although in Deut 14, they could be converted into money, but only temporarily - if the household lived too far away from the designated gathering spot to carry their agricultural tithe there; later, the money was to be used to buy cattle etc, so actual money wasn't given, as we do today.
This discussion prompted me to do a google on tithing and I came across a point I had never considered before, admittedly in an article that was clearly anti-tithing, especially to those of televangelist caliber.
Anyway, that point was, none of the NT letters discussed tithing, or used the word at all in reference to giving, and Jesus only mentioned tithing twice, both times in condemnation of the Pharisees. You'd think they would at least have used the word in context, if it was important pertaining to giving, which they discussed a bunch. And none of the early church fathers did either.