Another option would be tapping out and then straight back in again at Clapham Junction (perhaps at the Grant Road entrance). Clapham Junction to Golders Green is Zone 2 with an OSI at Camden Road/Camden Town which might save you waiting for the OSI to time out.
The other thought that struck me is why you aren’t starting your journey at East Putney or Putney Bridge, which offer straightforward non-Zone 1 options.
