Melessa, this is a tough spot to be in. Facing adversity in a child's education can bring families together or tear them apart. You and your DH may want to sit down and map out each of the possible strategies you see before you, and brainstorm on pros, cons, and possible outcomes. You may already be doing this... but I will elaborate a bit because many families read these forums who do not post and therefore these ideas may be of benefit to others.
For example, one conversation starter may be diagramming options/outcomes such as:
1. Appeal & stay in public: pros/cons......... what might this lead to... best case scenario... worst case scenario.
2. Don't Appeal & stay in public: pros/cons.. what... best... worst.
3. Homeschool: pros/cons...................... what... best... worst.
4. Private gifted school: pros/cons............ what... best... worst.
Gather all the information you can, and plan to speak frequently about difficult choices and their ongoing impacts. Your family may find that you need to be a source of strength for each other, as each person may have different risk-tolerance and sensitivities in facing ongoing educational dilemmas/roadblocks.
As a family you may wish to discuss the options you are most comfortable with (those which help you feel most resilient versus stressed to the max and unable to handle the next curve ball life may toss at you). Determine which options will stay on the table for further discussion and consideration. Have you utilized the Davidson Guidebook resource:
Advocating for Exceptionally Gifted Young People?
I second the suggestion made by another poster to contact a local homeschool group in your area and talk to those parents. See what their experiences have been if/when homeschooled children entered the local public school system at some point. Also, do local homeschool children participate in intramurals, community park and rec sports, or other events which might include kids from the public schools?
If you homeschooled for a bit and the local public school did not want to acknowledge your child's studies, might you have the opportunity at that point to enroll your child in the private gifted school? Would the private gifted school acknowledge home school learning? Would they administer placement tests or evaluate a portfolio? You may wish to tour the school, see if your son is interested in shadowing for a day, and apply for admissions, in order to learn more about the "fit" and how easy the school is to work with.
Here's hoping that facing this adversity together strengthens your family.
Here's problem with homeschooling for a year, learned the hard way at our house.
Schools won't accept courses that aren't taught by accredited institutions... In their minds, there is a procedure, and it must be followed. Anything off the path doesn't count.
I already posted a cynical explanation of why they do this. But suppose they are acting in good faith and are reluctant to give credit because they want ensure that students properly learn the material. Is there documentation they will accept, for example a student notebook with completed assignments, supplemented by a proctored exam?
Val, this is especially chilling because, if I understand correctly from other posts on the forum,
you may be more qualified to teach math than many/most licensed math teachers at accredited institutions?
Bostonian, I agree. Demonstrating knowledge by proficiency testing or essentially submitting a portfolio are respected and time-honored approaches. Given that Measures of Academic Progress (MAP) tests and other computer-adaptive tests are broadly in use by schools, some may say there is no legitimate reason or excuse for a receiving school to not provide an incoming student with some means of assessment, and place a student accordingly, regardless of prior learning environment. As an alternative to evaluating a portfolio or administering MAP tests or other computer-adaptive tests to determine placement, a school's end-of-term test for each subject could also be used for placement.
Refusing to accept a students' accumulated body of knowledge simply because the student's learning environment was not accredited may be a case where practices may work against educating minds for intellectual independence. Censorship, one-size-fits-all-education, and in some cases accreditation and credentialing may tend to discredit fabulous paths of self-education while acknowledging a potentially narrow or limited path of prescribed learning dictated by those in power and control.
There may be an emerging trend of schools wrestling power and control from parents. The larger the proportion of disengaged parents who are not supporting their child's education, the wider the door is opened for government schools to oversee and monitor parenting. Many districts offer parenting seminars, schools may record educational, demographic, and personal items into longitudinal data collection student information systems, and schools have the ability to monitor inside the home via school laptop video cam and microphone.
It is my understanding that to maintain any semblance of parental authority into the future, parents may need to keep an eye on legislation, and be willing to contact their State and Federal representatives. Ensuring and expanding parental rights, including the right to home school, is key. 
