I am looking to get some cast bullets for a 404 Jeffery, groove diameter .423". Cast bullets in this size go for about $.50 each. However, I can get bullets designed for a .44/40 that are .427" for about $.10 each. Since these would be used for plinking and general familiarization with the rifle, accuracy and terminal performance is not a significant issue. I am wondering if a cast bullet could be reduced in size by .004" in a lube/sizer die without a serious difficulty.

I have been routinely reducing .429" jacketed pistol bullets to .423" for use in my .404 Jeffrey, using a two step procedure and two Lee bullet sizing dies. By coating the bullets with lubricant and letting them stand over night, the effort required is reduced no greater than that of resizing a cartridge case.

The Lee dies work in a loading press with the increased mechanical advantage of such a press. I wouldn't try that much reduction in a Lubri-Sizer set up, particularly with using a hard alloy like linotype metal or wheel weights.

I sized a lot of 429JSP to 416 with one pass with a Lee push threw sizing die

I used a good sized press to do it I would not use a lubri-sizer to it.

Doing again I most likely add a 423 die into the mix just to make it easier.

So with cast bullets and a decent press should not be a problem.

Since cast slugs are normally sized .001-.002 over groove (IOW .424-.425 in your case), that's not much for a slug that drops at .427.

I've been resizing Jacketed bullets from .416" to .411" by passing them through a .410 sizing die and get about .001" springback. You shouldn't have any of the springback with lead.

Yes, back in the dark ages before we could get 9.3mm bullets I was swaging 375s down to .366, and .429s down to .412 for .405 /Winchester. You will have no problems.

The nearest without going larger, size for a LEE push-through sizing die is .410". How feasible an idea is it to get a .410" die and hone out the internal portion to .423"? It is too small an area to get a wheel cylinder hone or some-such in place so I'd probably be reduced to using a Dremel tool with small stone.

I made my 416 out of a 410 polishing it out with fine emery paper.

Shooting cast bullets that are 0.004-0.005" over actual groove diameter is not a new thing. The issue would be if the bullet/case diameter would fit.
It is possible that you can use the bullet as-is. Usually, lead bullet need to be at least 0.001" over actual groove diameter and 0.002" is often better.
Lee will make a custom bullet sizing die.

Not a Dremel that won't work. Use a split stick with emory paper in it; preferably with the die spinning in your lathe. Made many of them that way. First boring them out to just undersize.

I have a Corbon die to reduce .429 to .423.

Oregon Trail Bullets sent a trial pack of .427" bullets, 200 grain designed for the 44/40. I tried a few through the Lyman .423 sizer die, having lubed them with RCBS case lube. I can use the nose punch from the .429 semi wadcutter to push the bullets into the die. Measured them and after wiping the lube off, they were just over .423" and the reduction was well centered. I haven't seen any load data for a 200 gr cast bullet in a 404 Jeffery so there will be a little trial and error based on loads used in similar cartridges. Looks like the SR4759 will get a work-out and I see about getting a 5# jug of Trail Boss. By next fall I should be real familiar with the 404.