Riveting stuff...

These hammer drive screws look good:

http://www.hansonrivet.com/w58.htm

headbadge rivets ebay US link

http://www.toolfastdirect.co.uk/acatalog/Brassed_Hammer_Drive_Screws___Type_U_Round_Head.html

From www.bikeforums.net:"I just reattached my headbadge on a 1983 Raleigh Record ..... the right size was 2-56 (i think thats width and thread) 3/16 long."

"I'll be interested to hear if the drive screws can be pushed out from the inside.....To test this I pushed the drive screws out last night on my Bottecchia frame. I used a long screwdriver and they popped out a couple of millimeters and then I could get behind the heads to coax them out the rest of the way. It took no more than a minute or two to get both screws out and the badge off."

"Schwinn used very small round head sheet metal screws for attaching the headbadges of some models, notably the sixties, seventies, and early eighties Paramounts. They were No. 2 x 1/8" Type B sheet metal screws"

I was reading that too. Definately a possibility. I'm also looking at model shops for mini pop rivets.