While your suggested options may work, they also have a high probability of introducing cracking that can ruin the anvil.
If you want to go cheap and not overly damage the anvil, why not just attach a hard steel cover plate?
Just thinking...

I googled this when I read the OP's question and saw that option of adding a steel plate.
Agree wit Tim and John
Hardface will likely leave a surface that is prone to li'l chips fly'n off in your face when you least want that to happen.
For most anvil work a nice ground smooth surface will do just fine. I would prolly rather grind/sand my anvil down once a month to keep in in prime condition... It would likely take 20 years to deform it to any unusable extent.
For fine anvil work like knife making, usually only a smaller surface is needed... Why not look for a piece of used Rail track and build one... They can be super simple to very fine indeed... A million mesmerizing YouTube videos about these anvils... Don't look unless you are committed to spending some time and falling in love. Anyhow... That track material, especially the old used stuff, is nice and deeply work hardened... Nothing but good reports from long time users.
If I'm not sure what the material is I check the hardness and depending on that I TIG using either a misslerod.
On cast iron Weld Mold 700 is a good choice as well.
With some preheat. Then I feel pretty safe.
-Thanks
not really sure if anvils are cast iron, most are forged or cast steel. Could be wrong but a cast iron horn might not take a lot of solid hits.
Long story short I work at an iron foundry and because we can do side projects in our free time I wanted to cast my own anvil. I got an old cast iron anvil from a freind who was moving and after using it noticed the work surface just does not act the same as steel ones. So I was trying to think of a way to make a better work surface. I know some early cast iron anvils had steel plates welded to the top but they would heat the top of the anvil in a forge or something for a while then basically power hammer it on to create a forge weld. I can't really do that. Welding just a plate on my concern was how little fusion was happening between the two metals.
Making an anvil is actually rather simple in concept, but difficult in practice.