What's the strongest way to bond a cable stop to an steel frame?

Don't use cable stops. The biggest load those stops will ever see is when you grab your brakes hard for an emergency stop. So you're likely to find out that whatever you did to bond the stops to the frame wasn't strong enough or fatigue-resistant enough at the absolute worst possible time.

And you'll never be able to know if your work is fatigue-resistant enough. You can only find out that it wasn't - and you'll know that only after it fails.

Run the outer housing the entire length of the cable. All you need then is a few tie wraps to hold the cable near the frame.

Beside a professionally done welding, clamp-on cable stops should be a reasonably reliable solution.

Do you already have the cable stops? If not, then you might consider looking for ones that are attached by rivets. That will reduce the amount of skill and tools you'll need and will still give you a pretty strong bond (although it probably won't be the strongest as per your question, that is still probably welding or brazing). You'll need to make sure the rivets are the right size for the depth and diameter of the hole, as well as being thick enough to withstand the shear forces.

The ones sold here have holes for two 1/8" rivets.

If you go this route, I strongly encourage you do your own calculations, but as a rough guide according to NASA the 95 percentile maximum grip strength for males is 729N. On my bike the brakes have a lever ratio of roughly 1:3, which says we can assume a conservative estimate of 2200N of maximum force applied to the cable stop (if you're a 95th percentile male, squeezing at maximum grip strength in test settings that is!). I'm pretty sure this is within the capabilities of commercially available rivets (the fact that these things are even available for sale, not to mention being commonly used on carbon road bikes is testament to that!).