The pickled daikon radish is what most sushi places serve
in the "pickle" or "oshinko" maki. (There are other kinds of
pickles btw, but very few places I've tried in the US offer
a variety at least for makis). Usually you find it refrigerated,
I am not sure if freezing is a good idea (it's supposed to be
a little crunchy so texture may suffer).
I would lightly steam carrots myself (there is a carrot pickle
now that I think about it that is good too :-).
The gourd strips should be a little sweet (they are cooked with
sugar and soy sauce). I've tried them plain (you buy them dried
and cook them up...frankly not worth the effort) and canned, but
never frozen. They are an acquired taste perhaps.
A suggestion (if you like sour things) is to find umeboshi (pickled
plums) paste or whole (pit them if you get them whole... try to get
the kind that look softer, not the hard ones that look like marbles).
You can add this to your cucumber rolls or (if they have a fresh
produce section) look for shiso (beefsteak) leaves to make umeshiso
rolls. One of my favorites!
Other nontraditional makis I like right now are thai (thai chili
sauce, thai basil, and sprouts I think) and kimchi (the pickled