I'm pretty sure no one is going to get you in any faster- that is just how things are running. If you mostly are interested in OT, then call your doctor's office and just tell them you want a referral for Ot, they can do it. Has your daughter had her 4 year old preschool screening yet? You could ask for that and they would do an assessment and see what you qualify- they have a pretty good handle on what is "normal" in 4 year olds.
I honestly don't think neuorpsychs are worth a ton- they help but mostly you already know what you know and it will just confirm and give some clarity. When my oldest was tested it did confirm that he wasn't a little ADD- he was seriously ADD and we got a few hints about his learning style but that was it. And we still had to figure out what to do. What I tend to tell parents is pretend it says what you think it is going to say, now what are you going to do? Sorry- it is really hard to get services right now. So many kids are having these problems. Let me know if I can help, BTDT.