I soon found out why I'd never seen the Idol Challenge, or the Swimming Kids challenge: I'd never converted a fourth village. Allow me to tell you that the Prima strategy guide, while nice in its own way, has several glaring flaws. One is that they do not inform you that these two challenges only appear after you have converted your fourth village. Another is that they indicate at one point that there is an extra Norse village somewhere near your initial touchdown site, but that's beside the point... I converted the Greek village, Khazar bit the big one, and I went on to deal with most of the challenges. The slavers never accepted my wolf, so that challenge never finished, but I did manage to convert enough of Lethys' villages that he got snotty and kidnapped poor Du'thanai.
I have determined that one of my favourite ways of stealth-converting a village is to pick up several large rocks and set them down in my existing villages. Once enough villagers have danced around them that they become artifacts - with the godly symbol glowing in red on them - I pick the rocks up and put them in enemy villages. If I can't reach, I have Du'thanai do it for me. Lethys erected Shields several times over his villages but they collapsed eventually and people went back to being impressed by the rock. It's slow, but it's steady and it does a lot of good.
Will report on Land 3 as events warrant.