Not just that, I'd also work towards getting NSW & Queensland Cup to the same number of teams - so that you could run THREE "inter-league" rounds.
I'd base them around hubs - so if there's (say) 15 interleague games, you could have triple headers at 5 different grounds, and make a Saturday or Sunday of it at places like Ipswich, or Henson Park, or Dolphins Stadium for instance.. maybe even screening selected matches or hubs on a channel (if the content is needed).
Another option is getting both NSW & Queensland Cup up to 16 teams each, and running a 2nd tier "knockout cup" running into & over Origin/rep window.
Weekend 1 - 32 teams, 16 games, maybe 4 games per venue at 4 venues? Select few games televised - two weeks before Origin, while NRL is running.
Weekend 2 - 16 remaining teams, 8 games. Select few games televised. Last weekend that NRL runs before being paused for Origin.
Weekend 3 - 8 remaining teams, 4 games (Quarter finals, during first weekend of stand-alone Origjn, all games televised)
Weekend 4 - 4 remaining teams, 2 games (Semi-finals, during second weekend of stand-alone Origin, both games televised)
Weekend 5 - 2 teams left, 2nd tier Knockout final - game played as curtainraiser to Origin 3.