Families share everything, except DLC

I bought Minecraft on Xbox Live Arcade, primarily for the kids. Being a downloaded title, it is playable on the Xbox according to certain rules:

1. I can play it on any Xbox, so long as I am signed in to Xbox Live.
2. Anyone in the family can play it, on the Xbox in the family room only.

My son has expressed interest in having some friends over on New Years Eve for a Minecraft party. We do happen to have a spare Xbox, although its DVD drive does not read discs. I have it in the office, where I play the occasional Arcade game.
To fuel my son's party, we basically have three options:

1. Let him use the living room Xbox, which will allow him to play but leave me with the one that doesn't read discs (so, no Halo).
2. Let him use the office Xbox, with at least one person signed in as me (so, I don't get to play anything, since you can't sign in two places at once).
3. Use the license transfer tool to transfer the Minecraft license only to the office Xbox, so he can play on that without signing in (except I don't know if it's possible to transfer a single license, and I wouldn't be able to transfer it back to the family room for the rest of the family for a few months).

Now, if the game was on disc... Well, then it would be unplayable on the broken Xbox. But that's beside the point. There's still no easy way for me to just let my son play an arcade game on an Xbox I didn't purchase it on, without me signing in on it.