My Shimano 9-speed bar-ends have an OD of about 19.9
My Leadtec moustache bars have an ID of about 19.6

In other words, things ain't fitting!

Did I buy the wrong-sized bars? (they are 25.4's)
Do I file the ends of the shifters, ream the bars, or buy different bars?

Think of the bar end shifter as three parts:
1, the shifting gizmo
2, the aluminum 'pod' that mounts to the bar
3, the expandable tubular thing that goes inside the bar.

You can mix and match any of those. I'd check whether either #2 or #3 will fit your bar. Certainly you can file #2 down, but you probably don't have to. If #3 doesn't fit, that is more complicated (you have to disassemble it and file the flat spots of each of the expanding parts).

I have some bar end shifters made for aero bars, which are narrower, and had to shim them to fit in my bars. I can trade you the narrower bits if you like. That is, I can trade you my narrower parts #2 (which are black) for your wider #2, and my narrower #3 for yours. Your #1 will fit on either one.

After a little searching it appears that the brand of bars makes a difference. For instance, I have some steel Nittos with plenty of clearance, but I wanted alloy.

I knew it was close, so I started by using a grinding wheel on the bolt ends...that job was quick and easy. Next, though, I had to relieve the inside curve of the three pawls, where they contact the bolt, since they were also too wide to insert. For that I used a round cutting bit in my dremel, which took a bit longer, but eventually I was successful.

Oh, and BTW did you forget to say thank you for the offer to solve your problem by sharing parts with you. I'm glad you solved the problem, but stay part of the community if you can.

The size of the bar at the stem clamp is irrelevant. Whether the bar is 25.4, 26.0, 26.4 or 31.8, it'll still be the same diameter at the grips.

The catch is that bar-end shifters are generally used on road bikes, whose curved bars are typically 23.8 mm outside the stem clamp area. Flat bars are typically 22.2 mm. The narrower outer diameter generally means a narrower inside diameter, and in this case it was too narrow.

Steel bars normally have narrower walls than aluminum ones, so it makes sense that your shifters fit into your Nitto steel handlebar.

Easy to get wrapped up in the problem at hand. I am glad to see the happy ending, and the report of the resolution is a great way to provide others with the benefit of the thought process and effort that resulted in success.

That said, we do enjoy seeing pictures of others' challenges and successes.

If the expandable plug fits, then you have choices. Depending on your skills, tools at hand and the amount of meat on the bars, you can either open up the bars for the shallow depth needed, or file the short section of the bar end down a bit.

If the expander plugs don't fit, go back to the drawing board because it'll be more work than is warranted.