-I have learned that the promotional cards for Fleet base game and Arctic Bounty will be obtainable again with the impending big print. Will gaming stores simply be able to apply to Rio Grande games to obtain these?
-Are there presently, or going to be, any more new promotional cards?
A B, I'm not sure where you got your information. Rio Grande games has nothing to do with Fleet. It is only available through Eagle Gryphon games and the games store who distribute Eagle Gryphon games.
As a kickstarter, I can assure you that you aren't likely to get a hold of the KS exclusives unless you get them from a kickstarter who doesn't want his/hers anymore. (I'm hanging on to mine)
There are, however, some mini expansions available that might deepen your game play and they are very reasonable through the eagle gryphon website that Xenothon posted above, including an Arctic Bounty 54 card expansion that you can pre-order. This includes cards that were previously only available to kickstarters of Arctic Bounty. (I couldn't find when it would be available) *It includes the First Mate cards that you were referring to.