I have the same problem. 2001 LX 4 Speed with 250k. It's been perfectly maintained. Drives awesome (slow), but theres this one hill, super steep and I've driven a few cars (especially turbos) that don't like it.
Funny thing is mine does the same thing. 2100-2200 RPM you can have it floored but it's not passing that.
^^^^^ In what gear? On the face of it....it hardly seems possible that your transmission will not shift down to a gear that will allow mechanical advantage enough to achieve engine rpm greater than 2200.
I'm not saying it isn't so, just have a hard time accepting it. But that is based on my vehicle and how it runs.