Have you considered supporting a stealth address scheme for Bitcoin? The problem is reuse of addresses, period. Bitcoin has solutions for this.
Stealth addresses seem like they give much weaker anonymity guarantees than Zcash, unless you only ever send and receive funds through stealth addresses with others who follow the same precautions.
http://sx.dyne.org/stealth.html
https://www.reddit.com/r/Bitcoin/comments/2r07hu/whats_happe...