We sometimes use the old 90 weight diff oils as well for nasty milling. We have a really special milling
oil we use for cutting stainless here in the shop, but we buy it by the 55 gallon drum and I don't know where to get small quantities.
As for carbide, we routinely mill out broken taps with carbide end mills. You have to have a very rigid set up, peck extremely slowly, and spin the end mill quite fast for it to work. Spinning the end mill fast is counter intuitive, but it is the only way we have had any luck. For those who are interested, we use an rpm of 3000-4000, peck of 0.010" and a feed of 1 inch/minute. I have milled out 1 1/2 inches of hardened tap many, many times this way. When you are done, it is pretty cool because you mill out the center of the tap and the teeth of the tap just fall out.
We use junk end mills for the tap removal that you would never believe would cut anything. But they do. They are completely fried when we are done. But we do save the part.
David