I tried Mediation with him first, to try to give him a fair chance at avoiding court (even though he has threatened me with court since I was pregnant!), but he was able to swoon and sway the mediator into basically telling me I was to choose from his options of schedules with our child, and all of them took time away from me and gave him MORE time with our child?
Mediation is to help the parents to find a workable middle ground. Since the mediator can't force either to negotiate, it may seem that you're the one asked to give up more. (If it is a less experienced mediator, the mediator may pressure the most reasonable parent just to get 'success'.)
Evidently mediation failed, so you didn't cave. That's okay. Mediation doesn't have to succeed. Actually, for most of us here mediation failed in the early stages of the case. The Ex was too entitled. Par for the course. The threat of court may not mean much to him either, but when it gets closer that impending threat may make him blink. Mediation or a settlement conference may work at that point. Hold to your terms of what you think is right and proper, in the interests of the child.
Present yourself as a reasonable but concerned parent, that you can't "gift away" portions of parenting just because the other isn't being reasonable. Actually, that's why you can't just give in, appeasing and acquiescing do not foster future cooperation, rather it enables even incites more boundary pushing.
More than anything I want him to be forced into being evaluated.
Yes, you or the GAL can request the court for an evaluation. Understand that any order you get would probably have you
both evaluated. A pysch evaluation may not be enough. It may only cover a person's mental state and not how it could impact parenting. Most areas seem to have a more thorough process available focused on the parenting aspect, a custody evaluation. It will be expensive but as long as you get an experienced professional handling it, it can give voice to the concerns you have that aren't being listened to as yet.
My court process started with a temp order, then mediation, then court parenting investigation, then the recommended custody evaluation, then settlement conference, then trial date set. All that two nearly two years. When I arrived at court on Trial Day I was greeted with the news that at least she was ready to settle. She had delayed and obstructed to the limit and now it couldn't be delayed any more. We hammered it out in a couple hours.
However, maybe the GAL is perceptive enough to recognize the situation? Hard to say either way at this point. Go in as the reasonable but concerned parent. Be the Problem Solver. Present reasons and strategies you think would be best for your child.