From the description, it sounds like the trans is in 'limp mode' (defaults to 3rd gear, and is only gear available; that's because 3rd is the only forward gear in the 4L60e that doesn't require electrical input).
Check the trans wiring harness leads (internal; connects to the valve body) for continuity; they can / do short out, on occasion. If you have an open, or high resistance, then replace the harness. I don't have the various values offhand, but there should be a document on this site you can download that's effectively an ATSC repair manual for the 4L60 -- it will list each output and its acceptable resistance range. Also check to make sure the connector on the outside of the case (round, gray plug with two tabs on the outer (passenger) side) is fully seated. This plug can be hard to view while the trans is in-car (one of those little extendable mechanic's mirrors can help, here)
The other thing you can check are the two shift solenoids ('A' and 'B', on the 'front' edge of the valve body) - they could be out (although it's pretty rare for both to fail at once.) Those connect to the harness, as well, so also check to make sure they're receiving voltage (and are seated properly, etc.).
They're also interchangeable, so you can swap & test, if desired (preferably electrically, not road testing -- it gets a bit cumbersome to snug everything back up, refill the fluid, road test, and wind up having to drain it again, if problem still exists)
Guessing you're seeing a correlation here -- there's a better than average chance that your issue is electrical in nature. Which is definitely preferable to a mechanical one, IMO.
If you had someone build the trans for you, definitely chat with them. 23K on a fully rebuilt trans is a bit early to be having problems with it, assuming one doesn't outright abuse it. That goes for stock as well as 'built' 4L60s. What was beefed up in yours?