I've made quite a lot of .25-20 single shot brass, (the parent for .22-3000 Lovell) by swaging down .223 brass. It takes a heck of a reduction to the head size, and I don't swage the rim - I stop short of that, because .25-20SS is a rimmed case.
My technique uses a .30-30 die I had, which has the right diameter NECK. I made a punch, which needed a pilot in the primer hole to keep it from shrinking, and then went to work on my small hydraulic bench press. The body of the punch is about .30-30 shape, so it keeps itself pretty well aligned as it goes home. A shoulder on the punch sets the depth. The business end of the punch is slightly concave. This keeps the rim from trying to fold back into a dish shape. (My first punch failed to do this.) The pin in the primer pocket is actually an inserted piece, pressed into a bore in the face of the punch. This made cutting the concave face a whole lot easier.
For my project, the cases have to be driven out of the die. I did that using another punch in an adjacent arbor press.
Slow work, but I've made about 500 cases so far. The die leaves a fillet right by the rim, which has to be machined off in the lathe, but after sectioning a few of these, I'm very happy with the amount of brass still there.
So, if you can find an ordinary sizing die with the right size neck, and you can make the requisite punch, and have an adequate press, you have your tooling.
Pick a die for a cartridge with a nice shallow taper between the shoulder and the neck - a steep one will require much more pressure.
If you want to reduce the rim, then your punch can be long enough to drive the case right through, and the driving-out step is eliminated.
Remember that a sizing die's neck will be smaller than the nominal neck size for the case, when choosing your die.
I have also messed with using commercial drill bushings for this task. It used to be that you could buy these easily at any mill supply house, but with the advent of CNC machinery, nobody uses them much anymore. They are now special order, but they can still be had.