baby gates don't do any damage to the doorways. Mine and not fixed in place, it's hard to explain but you expand them and they are held in by pressure no nails or screws.
I was thinking that he may be able to be confined to a kitchen and use wee pads by the back door or if it is a sliding door you put a pce of dowel in the track so it cannot be opened any wider than required for the dog to get in and out. My mum does this for her little dog.
My baby gates are put up whenever we've got a litter and will be removed after winter as I have very pale carpet and the paw prints drive me mad.
It may be time to try a collar if your neighbours are getting narky, I like the air ones as the citronella ones leave the dog covered in the smell and they can sometimes become accustomed to it. Your council may rent them out.