On my wife's 99 B2500, the engine is revving up to 3-4000 when the clutch is engaged and/or shifted into neutral. Not all the time, but getting worse.

Most of time will rev up to 3000, then go back down to idle, but as I said, getting worse and taking longer to get back down to idle.

Any idea what would be causing this?

 

The computer is programmed to hold RPMs high when shifting, but only for a few seconds.
Try tapping the gas pedal and see if RPMs drop, if so lube the cable ends and the throttle plate, could be sticking.

Computer also will hold idle at 1,000rpm until speedometer drops below 5mph

Does the engine idle normally?
750rpm when warm
1,000rpm when cold

The TPS(throttle position sensor) is a long shot but might be worth testing, volt or OHM meter, or a live OBD II reader can show if it's voltage is changing when clutch is in.

IAC valve is another long shot but these can be cleaned.