We are the champions

One of the rarest items in RuneScape is a champions' challenge scroll. There are 13 lower champions, for which you need a scroll, 2 champions of champion, which require the defeat of a certain number of lower champions, and an informal champion, who only requires entry into the Champions' guild to fight him.

The most difficult part of this is actually getting a challenge scroll. You can camp for days/weeks/months, killing thousands upon thousands of zombies and receive nothing more than experience for your effort, or gain a scroll. You can be escorting the adventurer from the Temple Salve to Burgh de Rott and gain a scroll from killing an undead lumberjack. There is no set method to receive a scroll; no helpful item to increase the odds of earning this drop. 

I am actively killing ghouls for such a scroll. I've been told numerous times to not do this, that I'd be better off going about my daily routine than spending hours outside Canifis. Considering my daily routine doesn't include regular combat and, on the off chance I take a slayer task, that Kuradal would assign me aberrant spectres (the only monster she offers that could drop a champions challenge), how am I to boost my chances of finding this rare drop?