Got a pic of the hydrometer? Some auto stores sell the little testers with floating balls. You do not want that.
I would skip the hydrometer and put the money towards a clamp on meter. That tells you lots of goodies.
How many amps is your charger putting out?
Do you have a mystery load you're trying to isolate?
Ideally you would have both. Just seems hydrometers are better for guys who closely monitor their batteries. Maybe a solar setup and they want to see what state of charge they reach on an average sunny day.
I suppose for your situation you could test and batteries and confirm they're toast. But you sorta already know that info by the batteries age and waking up to 10v. Sure you could bust out gloves and play with battery acid. I do it more for fun than anything. If you want a super fancy hydrometer check out the Hydro Volt. Made in Germany and auto compensates for temp. It cost around $40 though.