The All Star 1209 is WAY too much rod for throwing any artificials along the So Shore of LI or Montauk--in fact, it's too much for every place you listed except the canal. While it would be OK for slinging bait at Assateague (give my old buddy Doug a hello while you're there
) you'd be better off with an 11-1/2' heaver. Like the Lami GSB 136 1MH, or one of those tweaked Breakaway rods Tres Irby sells.
Rather than chopping up that heavy, weepy Seeker, why don't you just start out with the 10' Lami SB 121 3M? That's a good jigging rod, it'll also throw big plugs and 6 oz of lead and a chunk. It's a good all-around rod, you can throw eels on it, plugs down to about 2 oz, jigs to 5-6 oz, bait, you name it. You can even get it in black, the model code there is BSB 121 3M.
The other two rods are OK for what you want. The Batson is the same as the Sabre 1208, lighter in action than the 1208 All Star, and a bit cheaper.
Instead of the E-glass MB 108, see if Mike can order you the S-glass version, the SMB 108 3M. If you get that one, you might not need the 10' 'tweener rod. Figure 1/2 to 2-1/2 oz on the S-glass rather than 1/2 to 1-1/2. There's maybe a $20 price difference, but IMO it's worth it.