The optional rule "Continuous Fire:" Why would you NOT use that (if being used)

[The Royal Hajj]

I also don't think this rule is particularly well balanced or thought out. My current opinion is the the quick pace of Continuous Fire should require both a Reload and Fire action dedicated each turn, so that ships can only sustain it if they're not using actions for repairs, muskets, or the other set of cannons. That seems to me a simpler solution than thirding damage (not that that's particularly difficult).

I actually like the requirement to plan both a fire and reload action in the same turn. At least that eats up some of your actions.

I don't see how the inability to reload after continuous fire is any different than the inability to reload after a standard broadside, so unless I'm missing something in the rules, there's no loss of pace there.

Normal ship firing over 5 turns
Turn 1: Fire and Reload action
Turn 2: Reloading
Turn 3: Fire and Reload action
Turn 4: Reloading
Turn 5: Fire and Reload Action
Turn 6: Reloading
Turn 7: Ready to fire

Continuous fire ship firing over 5 turns
Turn 1: Fire
Turn 2: Fire
Turn 3: Fire
Turn 4: Fire
Turn 5: Fire
Turn 6: Reload Action
Turn 7: Reloading
Turn 8: Ready to fire

By doing continuous firing, you are one turn behind the curve for firing at your next target. It's a small penalty and very situational, but it's there.

Doing half damage on the reload turn and half damage on the fire turn does not lessen the total damage dealt over two turns, and I believe it actually increases your odds of filling more target boxes. For example, say you have a ship that fires a broadside of 6. In a single broadside you pull a 4, 2, 2, 1, 1, 1. Against a 3 burden ship, you will apply the 4 for a box, then both 2s next for a box, then the 1s for a third box. If you split those same damage chits over 2 turns, your worst case scenario is 3 full boxes, but if you split the 2s on two separate turns, you're going to fill a box with the 4, a pair of boxes with a 2 and a 1, and the remaining 1 will spill into the third box. Simply put, if you can deliver the same number of damage chits to a target by multiple methods, it's better to break the damage into as many turns as possible, and it's better to deliver damage earlier than later.

I think your example of an SoL firing on the lightest weight frigate exaggerates the effects, but I think you are right that you will come out ahead more often by doing continuous fire. The draw of chits will of course play a major factor in it, but that can swing in both directions.

[Pseudotheist]

By doing continuous firing, you are one turn behind the curve for firing at your next target. It's a small penalty and very situational, but it's there.

Again, I could be misreading the rules, but I think your example is off:

Turn 1: Fire and Reload action
Turn 2: Reloading

should simply be:
Turn 1: Fire Action
Turn 2: Reload action

And in the second example:

Turn 5: Fire
Turn 6: Reload Action
Turn 7: Reloading
Turn 8: Ready to fire

you can scrap turn 7, so both ships are ready to fire on turn 7.