Yeah, HD rims like the tandems are .105ga, the Whizzer rims are .120ga. At one point there were oversized nipples to adapt down one size. I've seen a few of the larger ones and had a couple sets of .105 to .080 spoke/nipple combos on some BMX rims in the 90s, but never saw them again. It seems like so many of those indispensable little parts are just disappearing...
I've gotten away with thick stainless washers before and I see thick brass ones on eBay now, they may flex and "walk" less, but man...they never turn out looking right to me. A bushing or grommet(check out SunRingle rims) would be ideal....they're not readily available though...even if you could find them in the right size, I'm sure they'd become costly pretty quickly too.
The rims you've got don't happen to be 24" do they? I'm looking for a matched set for my whizzer.