I got an Alloy Y frame, it had headset cups in it, but no forks. I fitted 1" threaded forks in there. Using bearing clips and top bearing cap bit that was in my box of bits. And the lower cone bit that was on the forks. It seemed to work. No rocking.
But I didn't get round to riding it.
I decided to try another set of forks, wanted a chrome headset to match the polished alloy. But the 1" chrome headset cups don't fit. As its a 1 1/8" frame, I hadn't measured it. Now got a set of forks in there with an 1 1/8" aheadset.
So if you've got a lot of headset parts. try mixing up the cups and cones.
I think some BMXs used a larger diameter headstock, with a 1" steerer tube and 3/4"...21.1mm quill stem. So maybe try BMX parts