Skip all of the rest of those miniseries and just read the New Frontier entries. Captain's Table books all stand alone anyway, and Double Helix theoretically has an overarching plot but it's really thin and mostly consists of vague foreshadowing for the NF entry anyway.
Read them both like they were just New Frontier books, and you won't miss anything.
(Definitely don't skip the NF entries; they're awesome and pretty essential. Same goes for Gateways later on - you definitely want to read the NF entry, as well as the NF short story in the concluding volume. Bunch of stuff won't make sense without it.)