MarkR
So sorry to learn about your challenges.
From what you describe I think it would be very difficult to convince the ECO on Sole Responsibilty.
This whole area is so very complex and very unique to each case that I would not want to predict any outcome.
It may well be worth having a local specialist attorney review the relevant family and civil codes.
In your specific case, the mother is legally recognised as having parental authority, not the father. That's why I think it may be worth having a specialist to help an initial review.
Having said that I think the biological father does have some room for objection.
Have you considered getting married? This status may be a route to legal adoption.
Again, ideally you would need to get the bio father's rights terminated.
Unless he agrees to it, you would likely have a hard time of it.
You would definitely need a specialist attorney to prepare the adoption case.
Maybe worth some research on what the legal requirements and processes are.
Then as Graham has mentioned these actions do deprive the father of his children, and from your post it does seem he wants to be a big part of their lives.
Maybe someone on the forum has a silmilar situation that they have resolved.
Don't give up. There may be other ways. Children born out of wedlock in Phils are often able to access less stringent restrictions in the Family Code and the Civil Code.
Sorry not to be able to much positive help, but just wanted you to know that your post touched me.