I need to get out more, clearly. But I'll keep up with your journal and comment when I've got useful stuff to say.
And now I do. You posted:
Forgot to warm up with pulldowns
4/3/3/2/1 (Rats! 1 less than the total for the last few times, and I still couldn't make 5 on the first set. When will I progress?)
Are you going to failure on the first set? It sounds like you want to get 5/4/3/2/1 or 5 x 5, I'm not sure which. But one thing I've found works is something I picked up from some Crossfit folks - plan your race, race your plan. Instead of going full bore for 5 reps on the first sets, failing and then trying to extend the run for the next sets, aim for a total and spread it across the sets. So you've got 13 reps in that last workout. Instead of trying for 5 next time, try for 5 sets of 3. Do 3, rest, 3, rest, etc. You might not get all 15 reps, but you're more likely to get 14 than if you push all-out for 5 and then slog through the rest.
For example, when I do Crossfit's "Cindy" - 5 pullups, 10 pushups, 15 squats, max reps in 20 minutes, I've gotten far better results from doing 1 round every minute and resting if I finish faster than by going all-out from the start with no rest. I burn out too quickly "selling out" instead of pacing. I still haven't nailed 20 in 20, but last time I tried I got much, much closer (PR by like 3 rounds) than I did selling out.
Hope that's helpful. It's really worked better for me - keeps me from pushing myself to failure, I get a reward for good results, and I can better judge my total effort. Plus it feels like a break to end the first set "early" but you end up doing more work in less time across the whole workout.