The usual way of doing a conversion between systems is to not try to reproduce the mechanics, but to look at what the mechanics are trying to accomplish or model and then figure out the "native" way in the new system for how that would be done.
Since you're using D6 Fantasy, you're presumably using D6 Fantasy's combat system instead of trying to emulate d20's BAB system and armour classes – in the same way, make up a rule that "feels D6-ish" to handle this adventure mechanic. That's all the original authors did, after all.
But even given that, it's not hard to convert the mechanic fairly faithfully because you're not trying to convert a single roll, you're trying to convert a series of rolls and the probabilities involved there make the conversion easy.
Consider that an accumulated total is actually going to be a bit of a bell curve regardless of how you roll the individual checks, because the average of a d20 roll is 10.5 and after a few rolls in the series, the total will be likely close to 10.5 times the number of rolls, because the addition of multiple rolls smooths out probabilities. Because of that, you can use 3d6 to generate 3–18 (average 10.5) and your accumulating average will end up being very similar after enough summed rolls.