Josh,
I had the same (similar) problem. Short trips, delayed alternator output (although I never saw 14.4 volts), dead battery every week. Assuming you checked everything with a 100% battery charge (75% is minimum for tests according to Bosch), you have a bad alternator. I replaced mine and no more midnight Sunday driveway charging for me. 4 to 5 minutes is way to long; around 10-20 seconds on a good charging system to reach 13.8 volts at ~1000 rpm.(at most)

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The Golden Rule

1984 300SD (bought new, sold it in 1988, bought it back 13 yrs. later)