The prayer thing is entirely unnecessary and Ultimates are already running up against the buff cap, you could manage the idea with the same system as the 100 daily dungeon allowances if you just tweak it to be weekly with one allowance for this specific content. That said Ultimates are way too hard for such a limit, even at the maximum alt cap per account and buying level skips it would take years and years. Also your idea doesn't mention if "chance" applies to a single wipe or a full lockout.

A challenge you can do once a week would be interesting as an info gathering exercise. Extreme difficulty fights would likely be the sweet spot for this.