Carolyn Rowlett

Wow.  Sounds like you have your ducks in a row, but the school refused to look at the ducks.
One question:  If you homeschooled for 5 years, how long has she been in the public school system?  Around 2 years?
Given that you seem to have the data, here are my suggestions:
1. When you state "lack of meaningful progress" are you talking about IEP goals or gen ed?  If you can point to lack of progress on IEP goals, that is an argument for change - placement, modifications, etc.  (Of course, IEP goals can speak to gen ed progress, such as reading level, but having them in the IEP is best for enforcement of change.)
2. Is the director of special education involved yet?  A lot of times just going up the chain of command will get things addressed.  Send an email to him/her with all background information.  "Up the chain of command" could mean going all the way to the superintendent and school board.
3.  When are post-secondary transition services required (or allowed - sometimes the requirement is 16, but can start as young as 14) in your state?  I would calendar to request a transition evaluation as soon as you can.  That will help to point out all the ways in which she is not prepared for post-secondary life.  If the school does an insufficient one, request an IEE.
4. Reach out to your state department of education (special education division) to see if they have any suggestions.  Also ask when you can request a transition evaluation.  Finally, see if they can refer you to any agencies who do pro bono advocacy.
5. If your state offers mediation or facilitated IEP meetings, request one or both of those.
6. If you can afford one, if the school district keeps dragging their feet, you may need to hire an advocate and/or attorney to force this issue by filing a due process complaint.  Sometimes just the filing brings the school to the table with more flexibility.

That's a tough one to answer without all the facts.  It sounds like you're ok with her progress in reading.  But as you state, definitely monitor this.  Is the progress she is making closing the gap with her peers and advancing her toward grade level?  She would need to be making more than a year's worth of progress in one year's time in order to be making sufficient progress.  Otherwise, she never closes the gap.  Also, how does your school district determine eligibility for an SLD in reading?  Sounds like response to intervention?  If so, ask what their policy is on how MUCH progress is needed to deny eligibility.  Finally, what state are you in and does your state have any reading/dyslexia laws in place that you can refer to?  Some states have strict laws reading reading that even without an IEP your daughter might be entitled to a specific type of intervention, which she may not be receiving now.
As far as the slow processing,  I tend to agree with the school that a 504 would be the appropriate path for that.  There are some brain practices, etc., that can improve processing speed, but schools usually address this with accommodations only.  It would be a fight to get specialized instruction and goals for slow processing in an IEP, and there's no guarantee it would be that beneficial.
As far as the math and spelling, with the school eval showing her to be "average," there is not much you can do aside from requesting an IEE (except, as you state, closely monitor).  Do you have other data regarding these areas such as grades, standardized testing, spelling test results, written work that you can use to show the school why you are requesting an IEE?  That way you can couch it in terms of "I understand your evaluation showed..., but I'm seeing..."  It would be hard in that case to blame (retaliate) a parent/child for requesting additional data.  If you don't have the data now, start collecting it.  That way your request is based on data/facts, rather than you just not agreeing with their evaluation (which I know is not the case, but it helps to avoid that perception).
I like your idea of signing the evaluation report/eligibility decision with a written explanation of why you have concerns that the team did not find eligibility.  Write this on the signature page OR make a notation on the signature page that there is an attached written statement by you.  A partial acceptance will NOT affect your case down the road for an IEE.  You can request an IEE at any time.  But once a year has passed, the school will have a right to do their own evaluation again if you request an IEE.

When a PWN is required is sometimes state specific.  So you might check your state department of education's website for a list of when they require PWN's (or just call).  It is possible that they don't need to send you one until the change is put into the IEP document.  A copy of the minutes should protect you from them withdrawing their proposals.
But there are other things you could do.  You could send an email outlining the proposals made and agreed to at the meeting in the guise of "hey, I just wanted to confirm what we spoke about on_____ since we're coming up on the annual meeting."
You could also ask for a PWN showing the agreed to proposals (the worst they can do is say they don't have to do this).
 

They need to provide a Prior Written Notice that they are denying your request for an aid.   They also HAVE to put your parent concerns in the IEP document.