I lived all my life in Europe but relocated to Nigeria nearly 2 years ago to be near my widowed mother. I understand what you mean about members being extremely needy, because it's the same thing in Nigeria. I hope I am correct in what I will now say, if I am not, please somebody can correct me.
The culture in Black Africa is to have numerous children, even if the couple can't afford to look after themselves. This will off course bring poverty, misery and suffering for the couple and the children. They then become a problem to themselves and to others. Added to this, is the notion that the preacher is a "miracle/magic" worker, so the people will offload their problems onto him. From what I know of Nigeria, there is no level of "financial enabling" that will be enough because the more money you have, the more the people will expect you to help them. And dishing out money to them will only make people all the more dependent and expecting handouts. If they are true Christians, God will open a door for them to work for their own money, but if they choose to have numerous children, they should know they may have chosen lifelong poverty. Also, they all have (extended) family. Their families know them best, and should be the ones supporting the more needy members, (not really you). Finally, much of Black Africa needs social awakening and our people need to ramp up our reasoning skills, and begin to hold our mis-leaders to account, and make them care about the citizens by providing basic infrastructure and social amenities. They can encourage themselves to citizen action with, "I can do all things through Christ who strengthens me". Take care