Your practical troubleshooting makes perfect sense. Unfortunately, the theory (in your question) isn't quite there yet...

The confusion comes from the "800 CCA" designator. This doesn't mean that it's an 800 amp-hour battery. Amp-hour is a unit of how many hour a battery can run at one amp. So a 7 amp-hour battery could run at 1 amp for 7 hours, or 7 amps for 1 hour. It's a measure of electrical energy.

CCA stands for "cold crank amps". This means the number of amps the battery can output when your car is started (if it hasn't been for a while). So you have a battery that can use up to 800 amps to start the car. That spec has nothing to do with charging the battery, except (MAYBE) that you couldn't charge it any faster than 800 amps at a time (which would be ridiculous).

So what you need to answer your charging question is the AMP-HOUR rating of your battery. To make matters worse, if your battery is (lets say, even though it's urealistic, it makes the numbers easy) 100 amp-hours, it may not be 70% charge when it has 70 amp-hours of charge. It's not necessarily a linear conversion like that. But it does follow the basic idea.