A custody counselor would be good if you CAREFULLY pick out one (or your L strongly recommends) someone who believes in 50-50. You can also check out the option to have the court appoint a GAL. There is right now some momentum back towards one-parent primary. But be very careful here because I have seen some child counselors/GALS that that always, always recommend primary custody to the mother, even in some tragic cases with crazy or addicted moms. Most are good and fair, but just be careful here.
In terms of negotiating custody, first of all I would not directly discuss/argue this with your W. You could say nothing more than "I refuse less than 50%" and "Im sorry you feel that way" and "Want a Pringle?". Literally, if you never say another thing to your W other than those 3 phrases for the rest of your life you will be good. Let your papers and your lawyer do your arguing for you. If you have a GOOD counselor, let them say it too. But she will fight anything you say, so just dont say anything you want to fight about!
In terms of actually handling custody, I would recommend you look up parallel parenting. Best solution is to keep this amicable and have effective communications between the parents, but I sort of doubt that outcome is really in your control. Parallel parenting is tough for young kids but with only one 9 year old she will be OK. It works especially well with week-to-week, where the hand-off is basically coming home to a different house after school each Friday. There are calendar apps out there specifically for handling custody situations and all necessary communication can be done through these program.
As for the alimony, you are in an at-fault jurisdiction, right? Usually adultery is a ticket out of alimony - either through solid evidence or bluffing. But I think filing no fault and offering 1-year alimony is both fair and smart. You are being gracious offering her a carrot, while at the same time if she fights you on primary custody then you pull out the big stick - filing with adultery on public record, no support, immediate removal from the home, you expose adultery to everyone, and you go for primary attacking her mental state. Even if you dont win it all, she would be financially wiped out. She may be crazy enough to fight, but her lawyer wont be.
