Here are a number of .375"(originally) factory bullets that have been sized down to .367" for my M46 husky. I didn't use Lee dies, but a single Pacific .222FL die, modified, of course and it works perfectly - 1 pass form .375" down to .367".

I attempted to make a die for a fellow in California using the smae proceedure, but could not get it to the diameter of .366" - only .368", using the RCBS FL die set in .223, he'd sent me.

Left to right, they are 220gr. Hornady FN, 225gr. Hornady SP, 235gr. Speer, 300gr. Hornady RN, and 300gr. Hornady Interbond.

I have also sized down 270 Spire Points, 300gr. Sierra Spitzer BT's, 300gr. Hornady Spire Point BT's and 285gr. Speer Grand Slams.

Some more light bullets for testing in the 9.3x57.
220gr. Speer 235(shortened and sized down);, 235Gr. Speer(dropped on it's nose);, 200gr. much shortened 235 Speer;, 220gr. Hornady FN and 200gr. Sierra FN.

About 30 years ago, maybe more, I experimented with sizing down .375" bullets to .358 for my Norma Mag. I used a set of CH dies (2-die set) for making 1/2 jackets for the .38SPL and .357 Mag. this met with limited success ad that was too much, but did work for the very short or shortened bullets, until I jammed a jacket inside the die. All I need to do is to rot it out, I guess. Still have it, of course.

Sizing .366's down to .358 would be much easier, of course. I seem to recall using the core seater die first, then the sizing/pointing die second. That's the die with the stuck jacket IIRC.