I've got an old T mag and use a newer single stage LnL. I threaded through a die through a bushing and the threaded insert and into the plate on the T mag. The thin points to the outside grip notches are about 1/8 inch between the notch and the crest of the threading. So technically you'll be good there. But the metal left between the peaks of the threading between the holes would be less at or a hair less than 1/16 inch. So for me that would kill the idea. It would be a place that would act too much like the serrated "tear here" line on a paper form.
The upper flanges of the inserts will also intrude on the nut and washer of the pivot. So once the inserts are in place you'll need to set up and turn some of the flange rims away to get back the room needed for the the center nut's washer.
You realize that this is going to call for some pretty seriously accurate setup and boring right? This isn't something you do in a drill press where you rely on the existing holes to center up the drill bit then hog it out. To ensure that the holes you bore in your mill are axially located correctly you're going to need to lock a die in place then indicate for center off one of the smooth parts of the die.
If the goal is simply speed of switching dies then buy some additional die plates. Additional plates only cost $70. Since the bayonet bushings are around $5 each that means it's only $40 more for a whole replacement plate.
If the goal is rapid die setting then the answer is to swap out the often less than ideal die nuts for the Sur-Loc pinch style rings that Hornady sells. Those will ensure that the die stays set since those rings are NOT moving.
Or since you apparently also have a full machine shop make your own pinch lock nuts by machining down then drilling and tapping for the pinch screws with 7/8 UNF nuts. You'll get two pinch clamp rings from each nut with ease.
If the goal is to be compatible with a LnL press and dies set up in bushings that you have already then I guess you don't have a choice.
Because of the lack of metal between the major thread diameters of adjacent holes that would be NOT left after cutting and threading you'll need to go with "plan B". That would be to turn away the threads on the LnL socket bushings and press them into place with some industrial assembly adhesive such as Loctite 680. By turning away the threads you'll increase the metal left between the holes from around something like .06 to more around .16 to .18. And that would be lots. To do that I'd bore for a light to medium press fit using a fairly fast feed so the surface is left heavily scored to better key with the adhesive. Similarly I'd cut away the threading on the outer bushings but leave a shallow spiral of the root of the thread for the adhesive to key into. By the time the stuff cures it should be like it's welded in there. Just don't work so fast that friction raises the temperature to around 300F
BUT WAIT! THERE'S MORE! I was just finishing off the part above when I had a nasty thought. Sure enough.... With the size of the flanges of the insert and the bushings on the dies the diameter is big enough that the flanges are going to overlap. Now you can cut away flats on the inserts to allow them to seat but the flange on the die bushings has to rotate so that's not an option. So it looks like you can't do this after all. The die bushing flanges will interfere with each other. You'd only be able to load alternate positions at a time. So your six position plate only will hold 3 dies.
Since it will require a full on machine shop with a mill to do this modification anyway you may as well look at the idea of measuring out the circle size of the existing plate and make a new one that has only 5 positions. That would allow you the room needed between positions and give you the room to thread the holes for the inserts.
All this assumes that you also have a LnL press of some form already and that is why you want to do this. If you don't then simply buying the Hornady Sur-Loc rings or some other brand of pinch lock rings will both make die swaps faster and hold the settings by securely locking in a self centering way to the threads. Something that the Lee rubber Oring nuts and the RCBS set screw style nuts can't give you.