I would think 5-6k is a little much. High output alternators usually have a low output at idle, this is normal. Do you know if the alt. is in fact a high output model? You might want to look at the pulley first to make sure it's the right size for that application. Smaller pulleys spin faster. Bigger ones spin slower.
I had a wrangler alt. built for a "stereo on wheels" type car a few years back, and the batt. light came on everytime the car was at idle because the alternator wasn't producing enough at that low of a speed.
Maybe this could be the problem (provided the regulator is still good)? Thats just a guess though.
The 14 - 14.7 volts IS normal. The alternator needs to output this much voltage to overcome the internal resistance of the battery and charge it.