I'd see if he has any scrap ABS from the kit so you can see what kind of prep work it will take to paint the plastic before you jump in and buy the whole thing.
Is it black plastic or is it plastic painted black? Some light sanding, primer and paint would probably work to turn it white if it's black ABS. But if it's been painted black it'll need more work.
TK 4510 sells neck trim, and I think you can also order it from Seals-Direct, but I'm not sure on the item number.
http://members.cox.net/appstronaut/tk4510_decals.html
I've used Rusto paints and then a Krylon clear coat before with no issues. I would wait plenty of time before painting with the other brand and try it on some scrap plastic just to be safe.
If they really overlap that much I'd probably pry them apart and trim it so the overlap is closer in size to a cover strip. Though if you're going that far you could also swap to a cover strip.
I think the convention is to use a pencil to space the tube stripes out from the "cheek" of the helmet. Look at Mike or Scootch's assembly instructions.