On the rare occasion that I need to start driving above 30 MPH before things have sufficiently warmed up, I've found that my transmission doesn't like to shift past 2nd at the normal RPM point until my ATF temp gets up to about 60-75*F and my coolant temp gets past maybe 100*F.
I just flushed my ATF and the fluid looked good, and I have no issues or other symptoms.
I experience "authoritative" (but not hard) shifts from 1st to 2rd, and reasonably smooth shifts everywhere else. (Although my "garage shifts" (R-N-D) feel a little lurchy/lungy, but doesn't seem problematic.)
What I'm getting at is, IFAIK, a delayed shift from 2nd to 3rd when cold seems pretty normal.
You can see what my fluid looked like in my build thread from post numbers 44 through 49:
Ol' Ruby build thread
https://www.toyota-4runner.org/3698318-post44.html
Best of luck!
EDIT: And regarding what [MENTION=646722]bmason8159[/MENTION] said above, yes, 2000-3000 RPM is not really very high for this engine. It just "feels" high since under normal conditions, our automatic transmissions shift at lower RPMs. (Too low/early for my taste...) I think you're probably fine.