Lumber (and fresh drill bits) in hand, we went back to work. Max hung out with his Amma (my mother) for the morning while I essentially assembled a giant lumber puzzle. The result is railing that easily withstood me running and jumping on it (my standard durability test) and that is the same style as the rest of the deck. Woo-hoo! Less than $100 and a few hours of sweat really paid off.
While I was at it, I also installed a very tall pole for the clothesline. I'd previously had it attached to the railing, but since I was redoing stuff anyhow I thought I'd make it official. It'll also make a nice spot for a hanging basket.
I still have to stain it to match, but that'll wait for another day.