Congrats on your new toy, Dave, and welcome aboard!
As you're finding out, the AI is just too much fun in one package to be so affordable and still be legal. Sounds like you've got the perfect winds to play with too. You've got a lot of fun ahead of you, but you already have figured that out.
For transport, the foam blocks you mentioned work fine for supporting the hull. I wouldn't be comfortable putting my hull and amas on the roof with them though. While the hull will be supported, I'd be worrying about the amas bouncing and hitting the car. I think that could, over time, also wear the mountings for the amas & the akas. The stress in this case would be opposite of what the amas and akas are designed for. They are designed to support the boat with the water pushing up on the amas, not for the amas to be hanging from the akas supported only by their shock cords.
As for the short length of line that you mentioned, is there a piece of line tied to the corner of the sail that is left exposed when the sail is furled? Since that is the only short length of line that I can think of on the AI, a think that might be what it is. Tie the line to the grommet at the clew of the sail (corner where the mainsheet hooks on). Then, with the sail furled around the mast, tie a knot in the line so that it will keep the sail furled when the knot is slipped around the plastic hook that is on the sail. If you already have such a line already attached to the corner of the sail, then I'm out of ideas on that one.

At any rate, good luck & keep having fun!
Happy Sailing,
- Jim L