It is possible to get a two year draft to Nethers to work on the assistant staff. The system basically is that a soldier (apparently from any regiment, and i've known at least one Marine who's done it) volunteers, and if selected is drafted to Nethers where they are are taught to do all the jobs that need doing on a DZ, so they learn to pack and teach packing, run an equipment store, run manifest, run DZ control, carry out plane refuels, etc etc. This is concurrent with them learning (via the RAPS system) to skydive and progress up to instructor level. The aim after two years is for them to be drafted again, usually straight to their parent regiment's parachute display team (The Red Devils, The Black Knights or whoever). So that would be a possibility for you if you were already in the army.
As a civilian, your options are actually probably better! Netheravon can get very busy and the staff are usually run ragged, so if anyone shows up demonstrating the will to learn the mundane jobs like packing, manifesting or helping run the reception office, they are usually snapped up the CCI Nige Allen and/or the APA Secretary Robin Durie. These are the guys to talk to about work experience for any length of time beyond just weekends, and as your experience grows you can apply yourself to working more in whichever part of the circus most appeals to you, whether instructing, rigging, packing or whatever.
As for your question about the atmosphere at Nethers, it can be a very intimidating and occasionally annoying environment for a new face, largely because a) it is always hard to be the new face anywhere and b) some (and I emphasise NOT all) of the people there have a habit of talking down, rather than just to you. This was certainly my experience when I started there doing RAPS a couple of years ago. But when you hang around for a bit and jump with a few people, you start to realise that a lot of the attitude is for show, which basically means it's nothing to take seriously, and as soon as you realise that, you can get on and enjoy the jumping, for which Nethers is acually very well equipped! I certainly would not avoid jumping there until you have given it a go for a couple of weekends, especially if it is as close as you say. I would kill to live close to any decent DZ!
The best way round the problem is to have a friendly face to get you started. I'm going to Nethers this weekend, so if you feel like coming down, just go to the manifest office and put a PA call out for Jon Hammond, and we'll sort you out with a decent weekend! What sort of stage are you at, ie jump numbers, FS1 or above?
