Ok, sorry. Had to wait until after work to post
Ok, so 1st off, yes to naval bombardment. Makes sense that NGFS would have similar restrictions as land units.
As to your original premise above, you can have all sorts of fun with this. Additionally, pre-industrial, this would make perfect use of trade caravans ( I.E. supplies needed for your collateral to keep going). I like the cool down that you have mentioned, but lets sneak in that "emergency ammo" from a supply train and give the collateral a 1 more turn when you just need it, Lol, could you imagine the look on a players face when the AI sneaks in a "reload"?. Not sure how you'd code it, though IIRC, the trade caravan <global defines> can be easily tweaked ( been awhile since I've messed with that).
Similar situation with NGFS, pre-Ind, load a galley with supplies, or send supplies to your flotilla, and boom, 1 more round ( or however you decide) of attacks.
Now, post Ind, Logistics tech can play a big factor here for your Arty ( and Naval), as you could easily tweak all types of parameters based on stack size/flotilla size. No real need to be just static across the board, as Ind+ warfare needs the logistics in order to maintain a continued offensive.
As for promos, how about something along the lines of Logistics 1, 2, 3, etc, or even Supply 1, 2, 3, etc. This will give modifiers to what ever rounds/cool downs you decide to toss out there. This would also work in the Mod+ eras when the players gain access to missiles, let alone giving you the option to tweak maintenance costs for what ever format you decide upon.
I realize that a lot of peeps play quick games, and that their games are usually decided early ( pre-mod), but for those of us who like to go to the end, I see this as a potential to get rid of some of the tedious "ho hum" of combat, and make a player focus on supply and logistics for continued artillery instead of just stack smashing.
Ironically, Dacubz and I were tossing ideas similar to yours back in the day when we were working on the TTT series. It would be nice to see someone else come out with something similar. Granted, Some mods have "Logistics", but I haven't seen anything approaching to what your wanting to do.
Appreciate the chat bud. I'll keep an eye on what your doing.