So you have 25.8mm or 26mm handlebars, and it is a big struggle trying to get them into a 25.4mm stem clamp. 26mm stem clamps are rare, or too expensive. You can use a 1“ spherical grinding stone drill bit (at least that's what I used; the white one pictured), to bore out the clamp surface to a larger diameter. There are also diamond coated spherical drill bits. Make sure the bit can easily slide into the stem, then adjust the clamp tightening bolt, until it just begins to drag on the grinding bit. Work the grinding bit back and forth until there is no resistance. Continue to tighten the clamp little by little, while grinding away material. I got to 26mm within 5 minutes.

You can actually spread the clamp a little bit. You can also spread it permanently. Aluminum is not very pliable, but you aren't going to spread the clamp a lot, either. Start with something that just fits into the clamp, and then lever it open, until you can fit the next largest thing. Turn the stem over, and do it from the other side, as well.

Using both methods, I think you could get the stem to be a whopping 31.8mm stem, such that you can use the modern handlebars. ​ It would just take more effort. ​ Though, I think it depends on the stem. ​Some stems are beefier than others, and have more material that you can safely grind away. The one I have, pictured here, is like that. I imagine if people try it enough, we would know if it's safe. You are certainly playing around with failure of the stem, where you don't particularly want it to fail. Keep a close eye on the stem for hairline fractures, so you don't have a catastrophic failure. In my case, I was taking 0.3mm of surface off, which is not much and I may be a little over-paranoid in this paragraph.

A few bicycle shops told me this couldn't be done, and I couldn't find any instructions online. I hope this saves a whole bunch of people with their older bicycles, who either can't find parts, or need to buy really expensive ones because that's all there is available. I paid around $10 for the stem pictured, on ebay. Shipping is a long wait.