The latest date has to be 12 months old if you want to donate the entire thing and exit the position. You can pick specific lots, but I can't tell you how many times I have gone to exit a position, and have to leave 3.456 shares, because I used to reinvest dividends. You are correct. Every lot doesn't reset.
Not a deal killer here, just experience with making it a lot simpler. SSD makes some other good points about when they take averages, even when you tell them to take the lowest cost. This isn't something the brokerage houses do ever day (to the detail us tithe payers take it). To me, it is easier to exit positions, or larger lots and get away from the tiny reinvested stuff.
Another thought - as things move up, the recent reinvested dividends could be in a negative. You NEVER want to donate a capital gain loss. Never, never, never. Loses you tax money.