Just a quick message, that might enable you to keep going for a while. Sorry I can't investigate fully.
I've just got back from holidays and have 129 outstanding email messages. After that I can get onto following up all the leads that I found while I was away.
There does appear to be some trick to the Billinge websites. There were two http://www.billinge-history.comhttp://www.billinge-history.com and http://www.billinge-history.co.ukhttp://www.billinge-history.co.uk. From memory one had a blue coloured Homepage. They were basically the same data except one had extra information on some local families. I had both bookmarked but at the moment only the second one seems to work. I'm not sure if this has the family links, but you could look thru for other websites.
Alternatively, use a search engine to look for Billinge. I noticed a couple of sites. You might also do a search for Billinge in Genuki or Cyndi's List or other genealogical sites.