If the ship used a larger capacitor the capacitor charge cycle would take longer if the power applied was the same. Since the larger shields generators use more power, it stands to reason they charge their capacitors faster given the capacitance being the same for each ship. The Anaconda should have the largest shield generator, and it should consume the most power. Perhaps that's because it stacks so many low level capacitors (shields) or perhaps that's because it has the same number of shields that are simply more powerful (larger caps). If the former is true, the caps should charge in parallel and should not take any longer to charge. If the latter is true, then the larger supply should charge the cap at the same speed as the smaller supply charges it's caps.
It should take the same amount of time for a fully kitted out Anaconda to fully recharge shields as it takes for a fully kitted out sidewinder to do so. I get the balancing, but no one wants a balanced Anaconda, not even the sidewinder pilot. We want something we will look forward to owning one day, something that large weapons will affect but Sideys will bounce off of like mosquitoes. That's how it should be.
The docking issue with shields is a tough one. I'd say you should manage your power consumption and priorities before adding modules, of course if you're upgrading the shield generator, you cannot have both going at the same time, however you could add a precharged one.
I never got an answer to where the charge goes. How is it dissipated? Same question for FSD charge. Once it's charged, you'd not be able to dissipate it without a storage bank. There's nothing in space to dump charge into except the battery where it came from. It should show as heat otherwise, and it doesn't. So you should be able to charge your FSD and keep that charge until you need it. The spool up time should be negligible, since you're at full charge and waiting for "throttle up".