Fencing dilemma for beech/hornbeam hedge

Not sure of this is a landscaping issue or gardening issue - but perhaps a bit of both...
My family and I moved into a new house over the summer and are thinking of installing some fencing to improve our privacy/security. We have about 60ft of mature beech hedge and about 30ft of hornbeam separated by our front drive. The hedging is mature standing at over 2m high and about 1m thick. We live in quite a rural area and have many 'visitors' to our garden including deer and local dogs. I also have a young family and would like to have a dog of our own soon so am keen to keep things out as well as in! Although the hedging is thick, its a little bit patchy and as we head into Autumn/Winter, our privacy will only get worse although I expect both hedges to hold on to their leaves quite well.
By adding fencing, I would like to increase our security as well as reduce the visibility of our house from the road. So I would like to ask 2 questions to the forum:
1. What type of fencing should I use. I have been advised to go for post and rail with either chainlink or dog fence-type wire below the top bar downwards. The fence installers insist they can set the fence quite far back into the hedge so when it comes to Spring it will grow through and will hardly be seen. I'm a little sceptical and concerned that they may either damage the hedge in the process or that the chainlink/dogfence will restrict the growth of the hedge (I have read elsewhere on a separate post that someone had a problem with leaf growth on a beech hedge next to fencing?) and it may not grow through properly and thereby destroying the magnificent view of a beech hedge in full leaf come the summer.
2. Which side of the hedge should the fence typically be installed. On the inside of hedge (i.e. where it may be viewable from inside the garden) or on the outside (where it can be viewed from the road)?
If anybody has any experience of this or just helpful advice, it would certainly be most appreciated.
Best Regards Alex

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