So the thought in requesting an IEE is partly that -- depending on how IEEs work in your district/state -- you may be able to get a voucher from the district that pays for the eval that you are discussing with the psych in May. When you talk to her, that should probably be part of the conversation.
I am sorry the school lottery did not work out, and even more sad for you that his 504 is not being implemented appropriately. It is a legal document generated under federal law, and expressly relates to discrimination against students with disabilities. I am not normally quick to suggest litigation or related strategies...and this move would likely torpedo any hope of working collaboratively with the school (but given what you've described so far, perhaps it's past being a factor), but you should know that failure to implement a 504 plan can result in complaints to OCR (Office of Civil Rights). If OCR decides to investigate, they pretty much have a free hand to turn over any rock they feel like, including in areas not expressly named in the original complaint. So schools and districts -really- don't like OCR investigations. If this is a direction you might consider, it would be helpful to consult with a special education attorney, who should also have other helpful thoughts on how to increase the likelihood of 504 compliance (perhaps less drastic ones). Your upcoming psych consult might know some resources, since often people in her position get pulled in as expert witnesses.