I am writing perfectly clearly, and leave it to you to put some effort into learning the topic-specific terminology, start by googling and you will learn a lot. Plenty of "DC Electrics 101" resources out there, especially marine oriented.
If you still don't understand some statement, ask specific clarifying questions and you will be helped.
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> 1.) is it possible the solar controller and the inverter charger are reading each other and then deciding to not charge?
No.
> 2.) should I isolate each charging system to see if one or the other is failing?
Sure for diagnostics, does nothing once each source is working correctly.
> 3.) should I isolate all systems and use the garage charger to bring the batteries back up first?
Garage chargers are usually cr^p, make sure it's adjustable and high amps, depending on the bank.
But yes, shore power gives higher amps, better control, quicker results.
> 4.) how long should I wait to reuse the hydrometer, to allow the water to mix in properly?
The mixing comes from high-amp charging, especially following Equalization protocol.
The resting, ideally 24 hours, is for accuracy of the reading.