I do not know if I am going to be much help. The link below has a number of alternator files however they are more for information than a solution to your immediate problem.
A few thoughts however - your Interstate Battery is probably OK. About the only way to know is to disconnect it every night and reconnect in the morning while keeping track of the voltage: a) right after you disconnect, and b) just before you reconnect. Remove the ground only as that is easy and safe. The disconnect voltage will always be higher than the reconnect number but day to day, not much different.
Re the alternator, 14.5 volts is not too much, and what the number is depends upon where you connect a voltmeter.
I have a ScanGauge II plugged into my OBD port. It reads maybe 13.9 on cooler days (+60F) and less, 13.3 VDC, on hot days (+80F). This is the way it should be as charge rate is temperature dependent. That brings up another "reality" - per the files in the link, my view is that most battery charging problems in the 3 and 4 relate not to the battery or the "alternator", but to the regulator built into the alternator. The odds are the people who rebuilt your alternator did not replace the regulator as there is no easy test to determine that it has failed. The old ways do not work on these new "smart" regulators, hence you have have a perfect alternator and appear to have a good internal regulator as well. That is the primary reason LR quit selling rebuilts - even their people did not recognize a good from bad regulator. The real reason LR quit was their rebuilts did not even last a year and hence they were not making money installing rebuilts.
In otherwords, you may still have an "alternator" problem as the smart regulator has default values that will allow the alternator to generate enough amps to run the headlights and most other stuff but not enough voltage to actually charge the battery.
Do not be skeptical of the multi day or for me, multi night charge idea. Even a perfect system on your LR, or your Audi, or your Bentley, or your ..... will not fully charge the battery. That is why Bentley and the other expensive car sellers include a CTEK charger with each new vehicle.
You may have a circuit that is drawing power all the time. Well you do, it is the door lock circuit, but that is normal and takes about two weeks of parking to **** the battery. There is a scenario where the rear hatch door unlock mechanism somehow sticks and continues to draw power all the time and kills the battery. I say that but note that it is near impossible to actually discover.
Do the battery trickle charge for a week thing before you start pulling fuses looking for a constant draw - that is not fun but one of the reasons their are forty plus fuses in your 4.
https://www.disco3.co.uk/gallery/thumbnails.php?album=3801
A few thoughts however - your Interstate Battery is probably OK. About the only way to know is to disconnect it every night and reconnect in the morning while keeping track of the voltage: a) right after you disconnect, and b) just before you reconnect. Remove the ground only as that is easy and safe. The disconnect voltage will always be higher than the reconnect number but day to day, not much different.
Re the alternator, 14.5 volts is not too much, and what the number is depends upon where you connect a voltmeter.
I have a ScanGauge II plugged into my OBD port. It reads maybe 13.9 on cooler days (+60F) and less, 13.3 VDC, on hot days (+80F). This is the way it should be as charge rate is temperature dependent. That brings up another "reality" - per the files in the link, my view is that most battery charging problems in the 3 and 4 relate not to the battery or the "alternator", but to the regulator built into the alternator. The odds are the people who rebuilt your alternator did not replace the regulator as there is no easy test to determine that it has failed. The old ways do not work on these new "smart" regulators, hence you have have a perfect alternator and appear to have a good internal regulator as well. That is the primary reason LR quit selling rebuilts - even their people did not recognize a good from bad regulator. The real reason LR quit was their rebuilts did not even last a year and hence they were not making money installing rebuilts.
In otherwords, you may still have an "alternator" problem as the smart regulator has default values that will allow the alternator to generate enough amps to run the headlights and most other stuff but not enough voltage to actually charge the battery.
Do not be skeptical of the multi day or for me, multi night charge idea. Even a perfect system on your LR, or your Audi, or your Bentley, or your ..... will not fully charge the battery. That is why Bentley and the other expensive car sellers include a CTEK charger with each new vehicle.
You may have a circuit that is drawing power all the time. Well you do, it is the door lock circuit, but that is normal and takes about two weeks of parking to **** the battery. There is a scenario where the rear hatch door unlock mechanism somehow sticks and continues to draw power all the time and kills the battery. I say that but note that it is near impossible to actually discover.
Do the battery trickle charge for a week thing before you start pulling fuses looking for a constant draw - that is not fun but one of the reasons their are forty plus fuses in your 4.
https://www.disco3.co.uk/gallery/thumbnails.php?album=3801