He needs face grooving, not axial threading. So it's the cross-slide feeds that matter. And unless he can put together a tandem set of speed reducing subheads (he can't), there's no chance that a powered cross slide feed on any sane lathe will be that fast.
Jay Moore, you've already been recommended to send it out to a shop with CNC gear. If you don't want to do that, there are some old-school (like 19th Century) methods that might serve, but you're going to have to improvise a bit. There is no hidden panel behind your lathe's threading chart that will activate the functionality you need.
What I'm going to describe can be done on either a lathe or a mill with a rotary table. I'm going to be lazy and give a generic description, instead of explaining every detail about how the lathe and mill setups would differ. This may be confusing.
First rig an appropriate milling spindle. On a mill, use the mill. On a lathe, mount something on the compound like a toolpost grinder, only with a milling cutter.
Now you need to synchronize a 75% rotation with a fairly short linear travel, whatever the effective annular width of your clutch plates is. You need to consider the mechanical advantage here. You want to drive with the least leverage, meaning the applied force/torque is less than driving from the other end, keeping in mind that you're not just going to move the parts but also force the workpiece into the cutter. (That's what partsproduction was getting at in the preceding post.) I'm going to guess that rotation should drive linear travel in this situation. That means disconnecting your cross-slide (lathe) or saddle or table (mill) feed screw, and using another mechanism to push/pull the slide. Depending on the size of your machines, this may be easier to do on the lathe.
There are a couple of ways to couple the rotation to the linear travel. Rack and pinion is one. A metal band winding up on a spool is another, as you can totally ignore the non-linearity due to accumulated band thickness on the spool. The ratio between rotation and linear travel is controlled (completely) by the pinion/spool diameter. If the ID of the annulus you need to groove is less than the necessary spool diameter, you can stack the pinion/spool right on top of your workpiece. If the annulus ID is smaller than the necessary spool diameter, you have to work around that so the spool doesn't interfere with the cutter. Put the pinion/spool on top of your rotab, then stack an auxiliary table on top of the pinion/spool to mount the workpiece on.
Oh yeah, the loose end of the band/rack needs to be mounted to the fixed frame of your machine if you're using a mill. If you're using a lathe, the loose end would be mounted to the cross-slide. And if you're using a rack, you need a guide to keep it from pushing away from the pinion.
For each cut, unwind the rack/band, take up the backlash, and index your part to the next groove. Engage the milling spindle and plunge. Rotate the work, which will wind up the rack/band and pull the saddle/table/cross-slide forward.
I think I would do this on a mill with a rotab, rather than a lathe, because the rotab would give a lot better control of the cut than trying to rotate the lathe spindle by hand.
OK, that was technique A. Here's technique B. Make a cam that follows your desired groove curve. Mount the cam on the faceplate/rotab. Mount a cam follower on the cross-slide/fixed frame. As you rotate the faceplate/rotab, the cross-slide/saddle will move to follow.
Here's technique C, which is a variant on technique B. Make a cam that follows your desired groove curve, double-sided aka slot cam would be wanted here. Mount the cam on your welding table. Build a 2D pantograph with a cam follower and a "slow-speed router head" suitable for milling, with just enough 3rd axis motion to disengage the "router" from the work.
If all that sounds like a pain in the ass, Jay Moore, send your parts out to a shop that has more appropriate equipment.
