Tilling is kind of controversial. There's a few approaches.
There's the 'modern' tilling practices, which it seems like you've been reading of - these involve discing the ground, which does a few things; it will interrupt the life cycle of weeds growing between the rows, it'll also break the surface-roots ( i cant remember the real name right now; i always seem to respond to this when im not awake
) of the grape plants themselves which is "good" for the grape plants as it makes them put more energy into repairing their roots and this can somewhat slow down their green-growth vigor. The problem with tilling, is soil erosion and abundant loss of soil vigor / nutrients. See, the people that till, also "probably" use chemical fertilizers - nothing wrong with it if thats your approach, but they pretty much HAVE to use chemical fertilizers because the soil cant sustain itself with the erosion (winds, with no shallow roots to hold the soil in place) and baking that the sun gives it (breaks down the nutrients faster)
And there's "Green Manure". These are crops like alfalfa, which fix nitrogen from the atmosphere and put it back in the soil (most plants feed on nitrogen, so this is opposite).. These are usually left alone until after they flower but before they seed, when they are either mowed/scythed/eaten down; sometimes these are tilled under but its very common to find this set up in till-less operations.
In a till-less operation, its mowed down and left to degrade right where it fell. Some people employ/keep sheep or something of that nature, but if you went that route I'd suggest just having them come by for a week and not try to jump the hurdles of keeping them yourself. They eat the cover crop, deposit their "goodness" and move on. This is one approach that helps to work away from chemical fertilizers.
This can easily (in your head) work your approach towards something of an organic/bio-dynamic approach, which isnt easy to pull off but I happen to believe in (dunno about all them bio-dynamic practices, but the idea/theory of it is honorable)
When you're reading, be careful to diagnose the
slant of the authors - most either support chemical fertilizer or organic/bio-dynamic practices. It's all good, relevant, and correct info. But if you take information from one system and try to work it into the other, its headaches and heartaches with a large dose of confusion until it gets straightened out. Not to say you cant mix the two approaches, to a certain extent, but like you've already found - how does one grow a cover crop if you till every 2 weeks? You dont
I dont remember exactly how far down 114 will go, i just spouted 20ft as an example in my stupor; a little investigation can answer that definitively for you though.
Glad to help, hopefully I didnt just confuse you