You clearly haven't been watching OWL and what the Zen's in that do.
Her healing would need to be increased to counter this otherwise you're basically making her worthless. With your changes her whole combo would do: 175 damage and that's assuming you hit every thing (melee-->shield bash-->melee-->rocket flail), less if you also get the shield damage reduction which would lower it to 160 damage. Then she's not doing anything much until her combo comes back up. Her role is anti-flanker and you're basically trying to get rid of what makes it work.
My only issue with Rein vs. Brig is that Brig can stop a charging Rein with shield bash. This needs to be changed. A doomfist punch against a Brig shield bash results in both being stunned but a Brig shield bash against a charging Rein results in a stunned Rein. I'd be much happier playing Rein in today's meta of Brig on every team if I could charge in without worry of getting shield bashed and destroyed during the stun.