I got the pump yesterday.
The good news: I'm now 99% sure my pump was the issue. I can hardly blow air through the pump at all. The old pump was nearly free flowing.
The bad news: The shaft is exactly the same length.
The so-so news: After more inspection, the spines in the gear side are really in perfect shape. The splines on the old pump look a little bit fatigued. So maybe the assembly will be like new, as good as that is.
I've tried to think of a way to extend the shaft or add a coupling/collar and attach it to the gear, but I think any effort there would likely end up being nearly as difficult as changing the gear.
I installed most of it last night and will finish up once it stops raining.