I would suggest something like this:
6 weeks of lifting 3x/week. Condition enough that you don't suck wind as preseason training picks up.
Once preseason starts, scale lifting back to 2x/week, up the conditioning.
Otherwise, you're fine if you can keep up with the flow of the game. Rugby referees need more overall endurance than anything. My coach in high school was on the short list to be one of the first US refs to ref at the World Cup. Don't know if it ever happened for him. Granted, this was Rugby Union, which is a bit different than League.
He stayed strong, did a ton of tempo work and ran drills and skill work with us in practice. He maintained a base level of conditioning with a few longer distance runs per week to build that base of work capacity and was good.
I only know this because I spent my off season with a few teammates running with him after school at the track several days per week.
Rugby has a more consistent flow than American football does. Even the stops are relatively short.
I guess the real question is.... How have you felt in the past? Do you feel like you're falling behind or do you feel relatively good after games?
And if you don't think kettleball squat cleans are difficult, I say, step up to the med-ball
- CJ Kim