I've been using them for years, I didn't realize people still used the Lyman M die anymore, since the NOE version is superior. To be blunt, they are such a good idea that is horribly executed. NOE's version that fits in a Lee dies is a fantastic idea. A plug that expands the case the full length of the bullet is a fantastic idea. Unfortunately they do not work that great.
The problem with the NOE plugs is twofold. First they are very long, and straight sided. They have a huge amount of surface to grip brass with. Secondly they come rough as a cob. It's like trying to seat a bullet made of sandpaper down into your case. In all my years reloading I have never stuck a case into a full length sizing die. In the few years I've been using these NOE plugs, I've ripped more rims off of cases than I care to remember. Besides being tough to use, the other problem I keep having is scraping lead. I've had people argue with me about this. Well, I'd love to hear a solution. I've got at least a few sizes in every caliber from 30 to 45 caliber. Every single one will shave lead. The .004 larger section is inadequate plain and simple. A flare is so much better, and I'm baffled why anyone would prefer the straight section to a flare.
I have worked out solutions though. If you want to use the plugs as-is, the first thing to do is chuck them in a drill, and polish with a fine sandpaper. Second you need to use lube. The soot from a fired case sometimes works well enough, depending on how much you are expanding. I like to give cases a shot of Hornady one-shot lube, an this works really well. Do NOT use cleaned cases. Dry tumbled cases would be ok, just nothing that cleans the inside of the case. As for the flare, the only thing I figured out is to run the cases through a second time with the normal tapered Lee universal expander plugs to give the cases a proper flare.
If you want to go a step farther, I've made some prototypes of plugs that are vastly superior. They do not need any lube, in fact they run through dry easier than a polished and lubed straight sided plug. I'll post a picture below of the approximate dimensions for a 44 caliber plug, which can be used as a general idea for other calibers. The key is really just cutting a recess so that you don't have so much surface area. I don't know how I could modify a plug to give it a flare. I used a plug .002" big, and polished the "expander ball" part down to where I needed, then used a file to kind of make it a flaring die. You will notice I also drilled out the center so powder can flow through. I see no reason at all for them not to have this. Maybe not everyone would use it, but it sure is nice to be able to flare, and drop powder at the same time. It is a necessary feature to use these on a progressive press, unless you have an excess of stations, which very few do. You will also notice I have a "modified" and "compromise" shown. The modified is about how mine turned out, or at least what I had in mind. The compromise I think would be even better, allowing the straight section, as well as a flare if you need more. I think it would also work better with an automatic powder measure.
I have contacted both NOE and Lee about making these. Lee considered it, but they are worried they will not operate an automatic powder measure, so they won't do it for liability reasons. NOE never has got back to me. I hope one day he considers it. For now I've more or less given up on the NOE plugs. I only use them for special instances. For the most part I'm back to using normal Lee expander dies, they work so much easier, and they flare adequately.
Modified NOE top. Standard Lee powder through expander plug bottom.