Hi,
As you say it will be a long job, and you have to hope for not too much pedigree collapse.
I would say cluster analysis is the way forward.
You are looking for lower cM DNA matches with people who do not share any DNA from your known ancestors. You want matches with siblings or descendants of Ancestors of your unknown. Ancestry now more or less halves the job with its parent identification.
You will then have to hope that enough people have built trees, to the point you can extend them. And then hope that you can triangulate.
The fact that you don’t know the father does not really change the process. It’s pretty much the same for any unknown match.
Build a tree backwards from a match until you find a shared family. It’s easier when you get to a common name, but the principle is the same.
I realise this is a bit rambling, but I hope you get the gist?