Wow, necro thread, Yan Lo has been busy!
I like what InvokeChaos has suggested for a trigger but a single feels like it would be enough. Burning still feels like the weakest of the generic upgrades and requiring a further would still be too difficult to line up. However, even with this, I don't think that you would see the model on the table. I ran a Shen Long crew for a while and I was finding I was getting much more reliable damage out of the Fermented Monks thank the high river style.
As others have pointed out, why they are not taken is due to who they compete with, looking at them as beaters there are so many other stronger options in the faction, for a stone more you get an Illuminated.
So I have a larger step to suggest. One of the main "comments" on the TT within the UK at the moment is that they lack the activations to be competitive. With the High River supposed to be fast and hard hitting, what about dropping the card requirement for the 3rd attack and adding in a zero which allows them to discard a card for reactivate.