If you did put radials on it you wouldn't like them. Contrary to popular opinion they do not ride better, in fact they are hard as concrete. They built the 1800 suspension to be soft enough to be able to stand to ride on it with radials, not the other way around.
I just put them on my '83 Aspy. Major improvement from the Continental Pilots that were on when purchased. Any reason why you wouldn't want to use them, other than they are on the expensive side (for me in Canada anyway)?
Dunlop EIIIs come in both radial and bias ply. I have bias EIIIs on my 1500. You might find radials that would fit the wheel but you'd have problems with swing arm clearance. Radials are wider profile than bias for the same size tire. The sidewalls bulge out more so the width midway between the bead and tread is greater.