Can I restore pedals with no nut inside the cap?

[Y282]

Got a set of union rat trap steel pedals, mid 80s and need to take up the play in them. I've got them off the bike and pulled the end cap off one only to be faced with what looks like a blind riveted/deformed surface washer where there would normally be a nut.

I'd really like to reuse these pedals, has anyone successfully serviced anything like this and if so, how?

 

[pigman]

Re:

I think they have plain bearings, ie no balls. The only thing you could possibly do is to hammer the rivet further down to tighten the play in the pedal. Despite their crude nature, they are quite durable.