My first thought would be to look into some kind of legal aid agency in your area. I don't know the particulars of your financial situation or the specifics of who may or may not qualify. However, even if you don't qualify for state or county legal aid referral who may possibly assist in covering payment for these kind of assessment services [which are sometimes provided in custody cases], it would be very likely that they would be able to refer you to low cost services.

The advantage of going through these steps is that you are very unlikely to find someone who would be part of what you seem to describe as a type of "good old boys" network that you describe having experience being stonewalled by.

I'm not sure what else to suggest, but if you go through agencies that serve people of lower socioeconomic status, you are less likely to run into professionals who have that kind of attitude. You might also call your local health and human services division and ask for a referral or an organization or clearing house list or index with services or organizations- if you do this it will likely mean at least a couple hours on the phone as you get transferred back and forth while the people on the other end try to figure out who you should be talking to [it is just kind of the nature of the beast], but someone there should be able to give you some helpful information at some point.

I'm not sure there is any standard answer to your question, but some of that might help you find your way?

ETA: One other idea is to also contact the law clerk of the judge who issued the order and ask for a list of several references. Then you can research the background of these places yourself and you are not being referred to ONE place. Sometimes in researching several places online you also happen upon other places that may be better suited.