LBT 55gr. Spitzer, gas checked and .225 diameter with wheelweight metal; sorry, I don't have one and haven't used that particular bullet, but if looking for one with the two cartridges you describe, that's what I would have cut. It's listed in their latest catalog.

I use a 48gr. LBT LFN .225 gas check for my slow twisted stuff (1-16/1-14) cartridges. It's not in the catalog and I don't know if he cuts the all out custom stuff anymore. I'm assuming these are both std. twist guns, as in 1-14 and 1-12?
I've ran that 48 and a 70 gr. NEI design to around 2,900 fps. with consistent groups under 1 inch. The 48 I've run out of the Hornet with 5 shot groups around the half inch mark. The 70 I've ran from a 1-9 222 Magnum at about 3/4 five shot groups.

You'll want a.227 (for lubing and mildly seating a gas check) and .225 die to size nose first and to concentrically swage on the gas check; accuracy won't happen without doing so. Same for hardness. 22's pitched fast need heat treated wheelweight metal as hard as you can make them, which is another reason for the gas check: it makes it possible to get speed and accuracy.

If you're just looking for 22Mag level stuff, it's still going to be as labor intensive, if you want any kind of accuracy, but the check can be ditched as long as you're still using hard metal around throat diameter. Another option for this level might be unsized bullets powder coated. I've never used that method with .22's, since I'm set up and have the bells and whistles to just run sized, lubed and checked stuff.

Powder coat at 22 Mag levels should allow using a plain base, not sizing eliminates the pitfalls of bending good bullets and std. hardball alloy will be hard without the annealing process making it softer, as wheelweights are prone to.