I pulled each section through the heddles as soon as I was done tying it.
(In writing this post, I realized that I don't photograph this step very often, partly because it's been too harrowing to stop midway and grab the camera. These pics were cobbled from 3 different tie-ons.)
Here's the old system where I tie all the knots and let them hang together until it's time to pull them all through at once. This is stressful, even though I know it will work.
Before pulling them through the heddles, I stick them to the sandpaper breast beam and back up the warp beam to get them under tension. This tension is tenuous, adjusted thread by thread until it's "good enough". As I advance the breast beam to pull the knots through, there's lots of futzing to get those knots through the heddles.
This is the new system. Each section is pulled through immediately after tying. It's simple for two reasons: I'm only dealing with 39 threads, and they're all about the same length so getting them under even tension is easy.
The end result is that I've removed one of the most harrowing and risky parts of the process and achieved good tension much sooner than before. Yay, experience!