To get to Forest Hill from Hengrave and Boveney you would need to go down Wood Vale or Brockley Rise.
However, non-residents hopefully wouldn't want to use these roads as they would be quicker to stick to Honor Oak Road. A few local residents (Devonshire Road or even Dunoon) might be tempted to turn right out of Hengrave rather than crossing the Honor Oak Road / Honor Oak Park (Cabrini) junction, but this is likely to be less than the number of existing users.
It would be possible to make Hengrave Road no right turn into Honor Oak Road, just to make sure that nobody uses it as a shortcut, I had thought it wasn't necessary given the other restrictions, and it would make it much harder for Hengrave/Boveney residents to go East, South, or North. So I would not recommend restricting this.
If traffic at the Cabrini junction was too bad then a set of traffic lights might be helpful, for people turning right out of Honor Oak Road. However, one of the advantages of this system is that far fewer cars would be turning into Honor Oak Road from Forest Hill Road, as it won't really lead anywhere.
But I don't claim that this proposal solves all the problems, I've just tried to suggest a solution that doesn't just push additional traffic onto other residential roads by closing off one or other end of Devonshire Road. As I said when I outlined the proposal, I don't really think most residents will want this, as it will be a bit inconvenient for many local residents.