Right, lets have another go:
You say the hedge is 2.5 mtrs, so converting that to Imperial, lets say its about 8 foot ish.
Up until about 2 years ago I had a garden with about 140 foot of 9 foot tall privet hedge.A very old hedge, but very healthy. Parts of this hedge were about 3 foot thick, this was the section that was entirely inside my own property. Nothing would grow under this apart from the odd chickweed. Anything else that needed a root developed more than say 3" just didn`t make it. The soil was compacted and parched, interlaced with fine roots and on one side at least shaded for most of the day. So about 2 feet either side of this hedge was just soil. More like dust actually.
The rest of the hedge adjoined a neighbours garden, and this was about 2`6" thick and same again, nothing would grow there except very hardy weeds. Not that they really tied, just the odd straggler.
Privet is not a greedy plant but it will survive where most things will not. When did you hear of anyone feeding or mulching a privet hedge?
I accepted the fact that nothing would grow well under it and just kept it clear and tidy.
Now if a hedge is of the dimensions you describe then the leaf surface area for transpiration is really quite substantial, and this is why the soil at the base is always dry. It will also be very poor in nutrients, any being there being utilised by all the fine lateral roots that you noted. These roots also have the effect of compacting the soil.
Now all this can be overcome to a degree by forking over the soil at the base, feeding with compost/manure and a regime of watering, but the effect of this will be to encourage the hedge to send out more roots to take advantage of this. and a physical barrier will need to be about 3 feet deep to keep the roots out of the area you intend to utilise.
You also mention cutting the hedge hard back to the 'centreline'.
This is something I did to the hedge mentioned above, this was done with a lopper, a tool just for such a task. The effect of this lopping was dramatic , not immediately but after a season the hedge came back twice as vigorous and sprouting new growth from practically ground level. So whatever you do to compromise this privet will merely invigorate it.........
You also mention that the barrier you are considering will help stop slugs. I doubt that slugs will be lurking under a privet..The soil at the base will be far too dry for them to survive there,
Also, having had such a hedge, I know that if it does have things going in its favour, lopping, mulching, extra watering and so on, it will put on a corresponding spurt of growth and this will of course need cutting back. With the right timing you can get away with 2 good trims a year on a privet hedge that is more or less otherwise left alone.
One that gets the treatment above will easily put out up to 3 feet of growth in a season. Mostly horizontally. The problem now is compounded for you because you will have to cut this back and what you cut will fall where you are trying to grow crops. You must be aware of the volume of cuttings from such a sized hedge, and there are not many veg that would thrive after such an amount of clippings has fallen on them the been collected from them, no matter how carefully.
Far be it from me to dissuade someone from growing anything, veg, flowers, shrubs fruit or whatever it might be, but nature has its own rules and these are almost always immutable and cannot be compromised even with the best of efforts and intentions.
There is one further point:
Often plants are used as foils, or even sacrificially, to attract pests that would otherwise attack the crop you are trying to grow. Well privet would have the opposite effect, any pests would ignore the privet and go straight for your crop. When did you ever see anything bother a privet? In fact steeped or boiled privet leaves make an excellent pest repellent.
Learn to love the privet and grow the veg somewhere else would be my advice, but you know that already don`t you? *S*