As a building owner, I have had lots of experience of PWAs. Built loft, doing a kitchen extension and a cellar conversion, all requiring PWAs with both neighbours.
You should insist on having PWA with photos etc and other specific requirements that you have (e.g working hours, access, making good, etc etc). This will form your civil and legal contract with the neighbour. After your PW surveyor has correctly served PW notice to neighbour, they have 14 days to respond. If they don't, the matter is automatically in dispute unless they respond and tell you they will appoint someone themselves. They have a further 14 days to apoint someone I think and after this your PW surveyor has the right to employ someone on THEIR behalf if they haven't named anyone.
To cut cost, you should persuade them to use your own PW surveyor, which is totally legit and he is independant looking after both your interests. This means you only pay for 1 surveyor not 2. Remember as building owner YOU are responsible for all costs of PWAs, making good, paying for their appointed engineer to check your plans, structural calculations, repairing damage that has been caused as a result of your development etc etc.
It also gives you the legal right to enter their property for doing the work by giving reasonable notice etc. Talk to them nicely but do all official work through your PW surveyor.
And yes it is impossible to stay 'friends' with your neighbours. I have fallen out with both of mine for now. Especially as one of them saw my works as an opportunity to improve their property at my expense and started to specify the most expensive bricks one can buy to build a section of wall that faces their house. I will never see this section of wall and was forced to meet their demands as they threatened to pull out of other agreements we had made so i saw it as an 'investment'.
The other neighbour complained to the council even though I had PP and now continue to find any opprtunity to whinge including telling my builders to stop work when I was away for the weekend threatening they will call Council - we were within oir legal rights to make noise until 1300h on Saturday.
All of this is after I had sent both neighbours, them full plans and PW agreements and gone round to talk to them a couple of times each.
In summary, PW agreements protect you,, they are worth teh money and if you ever sell the house, they will be required to be submitted with the deeds to the new owners.