I am writing to kindly ask a question:
how can I start on the homeschooling path with a classical education curriculum, given certain personal parameters?
This is my main question - and I am grateful in advance for any kind of clue, advice or starting point suggestions.

To provide a bit of background...

I have a 10 year old son in the Gifted program and an 8 year old daughter who clearly qualified for the program based on her ability and achievement scores, but the school disqualified her with a teacher-filled "motivation" scale which was 100% intentionally misjudged - set right below the qualifying point. The mountains of evidence (both external and school-based) we brought in support of her huge motivation abilities did not move the school or the district - but this is a different and largely irrelevant story.

Ever since my oldest started K, I have been dreaming of homeschooling. The wish to home-school has been 100% related to pedagogical and disciplinary substance concerns, and not to ideological or religious reasons. It is also related to the fact that my oldest (4th grader) is "twice-exceptional" - both gifted and ADHD-diagnosed. He typically comes home either with grades in the upper 90's-100 or with 0-s, when he forgets to turn in worksheets or to complete a task due to getting off track. He is extremely easy to distract, impulsive, too busy being the class clown, simply put: a hot mess. The girl is doing very well but is stagnating without any challenge - not even the once-a-week little extra my oldest is getting.

Having been raised in a radically different educational system overseas, I, personally, have been severely disappointed with the "lowest-common-denominator" pedagogy of public schools - even though my children attend a very highly ranked one, in a very good school district. Higher-income housing in the area notwithstanding, I find the pedagogy and curriculum seriously wanting. If I have to summarize it one word, what comes to mind is "fluff".

I dream of a classical education where rigor, solid canons/foundation, mental discipline, good study habits, serious problem-solving skills and elegant disciplinary substance prevail. I have now had the kids in public school long enough to know that what I have in mind will NEVER happen, no matter how I twist it. Their education is loose, flabby and random skill-based; it boils down to multiple choice, glue in, fill-in-a-blank and circle-a-word - here and there.
I am
desperate for more for these kids but knowing I will never afford an elite private school, I can't stop thinking of homeschooling.

The only reason I haven't taken any step in this direction so far is because I must also work. Not work as in "I am a career-woman at heart", but work, as in "I must also provide for our family because my husband's salary alone is simply not enough for our family's long-term needs".
Within my "must-work" parameters, I have been lucky enough to pick the best profession I could have possibly picked. I love what I do, I am good at it, it is difficult, but the autonomy is high and the schedule is also very flexible, including a good amount of work-from-home.

I work as a university professor and this year I hope to obtain tenure with my current institution. Pre-tenure, the loads are beyond rough, including week-ends and many all nighters to maximize publication record; but after that, the pace becomes less frantic.

As I have been approaching the Promise Land, I have begun to seriously consider homeschooling in the morning (4 hours max) and to do my work after 12:00 pm, including scheduling my university courses in the afternoon/evening, twice a week.

Had I had an 8-5 job (make it 7 with traffic, having been there) - the homeschooling would have obviously been out of the question. I realize, however, that even with my flexible job, I may still commit to an insane regimen, becoming both K-12 teacher for an elementary and middle-schooler, and university professor... and cook (because we've tried the frozen dinner route and I had to gibe up after a few months).

I have no idea if there have ever been other homeschooling moms in this type of situation, whether this project is even realistic...how expensive the curricula materials would be, etc.

I would only want to homeschool the kids through middle-school and have them back in public school by 9th grade.

Please let me know where I stand on an insanity scale from 1-10. If my average score is reasonably close to the lower-end, where do you think I should start?

Thank you so much!