As stainless steels go 303 & 304 should machine quite easily. My suspicion is that maybe your die was on its last legs anyway and was forming the threads as much as cutting them resulting in a degree of work-hardening, that or you didn’t get what you thought you’d got!
If you have access to a lathe it is worth roughing threads and finishing with a die or better yet a dienut. Even a half cut thread will take a lot of the load off the die and the tougher the material the more it is worth making the effort.
It is worth noting that few dies will have more than 8 cutting facets and that means even on a 26tpi thread each cutting edge is taking a 0.003” cut off both flanks of the thread. If I were screwcutting such a thread that is about twice as much as I’d choose to remove off one flank per pass.
Another point is that a 70% thread, (effectively one missing the radius on the top), still retains about 90% of its maximum strength but requires far less cutting effort. On difficult materials it is therefore worthwhile reducing the nominal diameter of the material before screwing. In any event there is always a degree of extrusion of the material with the cutting action so it is good to have somewhere for it to go.
If you are really stuck I have a small supply of stainless in various sizes so I might be able to help.