But doesn't a mid-20s K number at a JKLM seem unlikely in any case?

OP, I think K is different from popular DCPS--they don't know how many people will register over the summer. I imagine that they won't move until August.

In-demand DCPS schools are very unlikely to admit many from the waiting list for by-right grades until after the school year has started, to preserve maximum flexibility. You may have a chance, depending on how balancing classrooms and class sizes work out, but I wouldn't expect the lists to move much this summer.

We're stuck in the mid twenties and high teens for a few schools for K for a few JKLM schools (and a few others). We have moved one or two spots on about half of them. I keep seeing these posts that people's numbers are moving a lot. Is it hopeless? New to this.