Sweet! After restoring a couple SS's, I'm pretty sure you won't have to purchase any ignition parts to get t running. I went into mine with the same thoughts as you and ended up not placing the order from Weber.
You can tell from the gas line pic it's full of shit inside. Take it all apart, clean it out, run sandpaper over the tube and that part will be ready for action. Same with the igniter. Clean the contacts with sandpaper, put the wires back on the button, and hold the other 2 wires in your hand. Push the button. If you feel "it" you'll know the igniter is fine.
My non-working 98 SS was just like you described and a simple cleaning got it reliable like it was new.
Good luck with the restore and have fun.