Using super-cutoff to reduce Direct Source to Drain Tunnelling
I have never seen tunneling from the source to the drain, but I have seen it in the high field that is generated from the drain edge to the gate.  I use tunneling on my floating gates, so I think I would have noticed the effects on my thin-ox devices.  What you seem to actually be describing is decreasing the drift current.

With a FinFET, you have the that magical 70mV per decade, and I'm not sure how much tunneling actually exists.  I make devices on a SOI process, but let's assume that you have a bulk process, so you could change the depletion depth.  You could change the barrier and thereby change the threshold, but then you have to ask about why you'd want to add the complexity when you could just use a threshold implant.  I have 7 different thresholds in my last kit.  This is one of those situations where I know a lot, but cannot tell you a lot on numbers, but let's go to the Kappa = 1, at 70mV per decade, if you bias the well by 70mV, you get a decade of current.