I agree with all the advice that has been given so far. I am a little unclear if your voltage light has just now begun to remain lit (until 1,100 RPM), or did it maybe begin with the replacement alternator? If the "new" alternator has always acted this way, it is very likely just a 'quirk' of the particular alternator.
If it just began after finding the battery totally dead, it MIGHT be from a diode failing. Almost every time a diode fails, it fails "open"; (ie it will not conduct electricity in either 'direction) but occasionally they will fail "closed" (shorted). If that happens, it may just have a very slight 'leakage', which will drain the battery over a period of several days, or it could develop a 'dead short' which could be bad enough to burn out whatever device protects the alternator's battery wire.
It is pretty easy to check for shorted diodes. Just remove the battery wire from the alternator (the heavy wire, fastened with a stud and nut). Do this with the engine off; and be very careful, because this wire goes directly to the battery, and is ALWAYS "hot". Hold the multimeter's positive lead against the eyelet of the battery wire, and hold the negative lead against the stud on the alternator.
The meter should read zero volts. If it reads a few '100ths' of a volt, you can most likely consider that the same as zero (make sure the meter is not reading the voltage path through yourself, ie don't touch both probes with your hands). If the meter reads a few '10ths' of a volt or more, it is (almost) certain that there is enough leakage through the alternator to drain your battery over a day or two.
If the meter is reading zero, keep the positive lead on the wire, and touch the negative lead to a good ground. Confirm the meter reads battery voltage.
All that said, 12.8 volts at 2,000 RPM, is not unusual in your given situation. It is very likely the replacement battery was in a state of discharge, and while I am not familiar with the alternator on a LB1914, I would guess that it does not have a terribly high output, so if the battery was (somewhat) discharged, it might take several hours of running (at 2,000 RPM) to see the full output voltage. Even then, I don't think you will see 14 volts; more likely mid to upper 13's. (IMO)
Good Luck! Let us know what you find.