Stanford published a paper that is basically the exact same model
Um yea.. "basically".
Except they demand an 'ultra-slow' hash function in that paper. You ignored that requirement and that makes your implementation equivalent[1] to using the same password for all websites.
2^16 rounds of SHA-256 might not be "ultra slow" but it's certainly not as bad as you make it seem. If you read the analysis in the article, it would take many years to crack a random password with this hash function. It's unfair to say I "ignored" that requirement.
Um yea.. "basically".
Except they demand an 'ultra-slow' hash function in that paper. You ignored that requirement and that makes your implementation equivalent[1] to using the same password for all websites.
[1] https://www.achilleslabs.com/product/4