Thanks for the tip regarding the 1099DIV, LOL. I might have overlooked the mistake and overpaid my taxes.
Regarding the overall mistake of buying the dividend, sometimes it's better to be lucky than good. After refining my calculations to include a higher tax rate for the non-qualified portions of each dividend, I see that each of the four ETFs I bought on 12/16 gained more to the close of the day before each ETF's Ex-Date than the tax on its dividend. Collectively the gain was 3.7 times the tax bill.
Regarding the question of selling at the close of the day prior to the Ex-Date and buying at the open of the Ex-Date, my taxes would have been 20% higher if I had done that for all four ETFs. That said, I could have lowered the tax bill by 30% if I had done a sell/buy for VEU and VWO only. That's a theoretical observation -- I was out of the country and not in a position to manage that complication.
At any rate, I feel pretty good about making a mistake, avoiding paying for it, and learning a lot that will be useful in the future. In particular, I see now that each Ex-Date is an opportunity to optimize, and I look forward to managing them in a hands-on fashion going forward.
Many thanks to all for the information, feedback, and support. You guys are great!