I don't think there is anything official regarding "back-up" characters in any WotC manuals or guides.
In this specific instance, I think you guys will just have to homebrew it, and decide what's best depending on your campaign setting, your DM, and your PC group dynamic. Either way, I'll try my best to answer your questions from experience:
If this is the case, though, how should we handle their experience? Should all backup characters gain experience at an equal rate as the player's main character? Should they level up at the same rate, but keep the minimum experience for their level?
I think that back-up characters couldn't possibly gain experience at an equal rate as PCs, because situationally, I don't think they'd gain the same XP in combat/story scenarios. If they did, then they would be as involved in the conflict as the PCs, which for story telling and role playing reasons could not make sense. But if you don't quite care for technicalities, then I suppose they could-- their XP might not be justly deserved though.
I also think that would lead to PCs taking death for granted in game; although many players take their characters and backstories seriously, many players care about the leveling up part of their characters. By giving them characters that are where they left off, it might create an environment where death isn't taken quite as seriously.
Is there a different way to handle this entirely?
I think that you guys generally have a reasonable idea; if your campaign is mostly set on the seas, I can understand why "back-up" characters who are crew members might make more sense than other more fantastical, Deus-Ex Machina-y reasons.
What I would personally do, as a DM, is perhaps set them at a level lower than their current PC was when they died, or set the new PC's level to be the same as the lowest level in the party.
There is also the idea that if you are on a boat, ship, or any type of seafaring vessel, at some point you will have to dock at a port-- to restock supplies, conduct maintenance, gather info, etc, etc. This could be a reasonable way to "recruit" new crew members to help fill in the gap left by deceased characters (and a reasonable way to introduce new PCs).
If you guys are open to using the playable races introduced by Volo's Guide to Monsters, a new PC might be a Triton, who guards the ocean depths and might want to join your quest, especially if it is set so close to home. A campaign set almost exclusively on the seas lends itself to including Tritons as a playable character race. I do warn against using these races so openly, as more impressionable players might want to be a "cool" new race, and then you'll have a party full of rare races-- though, if you know how to work with it, that could be fun too.