"I am a college professor of mathematics who has done course development work in mathematics eduation."
As a college professor, I would expect you, of all people, to appreciate the fact that education should not be compulsory. Anything of true value in this realm will automatically be supported. But the compulsory aspect of it is what has brought the negative aspects of it to bear, such as the NEA and all the social programming that comes with it.
Since you have read Dewey, then you may be familiar with this quote:
"independent, self-reliant people aa counter-productive anachronism in the collective society of the future."
and this one in which he praises the Soviet school system:
"That which distinguishes the Soviet system both from other national systems and from the progressive schools of other countries is the conscious control of every educational procedure by reference to a single and comprehensive social purpose."
These quotes are not pulled out of context, they represent what he and many other preeminent educators of the time thought (Horace Mann was not as convinced of the need for compulsion -- he was more interested in persuasion, but he agreed with the collectivist ideals). The prominent educators were enamored with collectivist, statist ideas, as were most of the intelligentsia. Dewey and others from that era are the reason that schools started trying to shape the culture through socialist ideals instead of just teaching the basic subjects.
BTW, your quote from Jefferson is immaterial. Jefferson only supported voluntary education, and his idea was not to indoctrinate students. He instead believed that students should be taught critical thinking skills.
"But you did not respond to my primary point -- that government support of science and science education is necessary for our national security."
I agree, gov't should support science education for many reasons, of which the most important is national security.
While I think K-12 should be compulsory, it needn't be public. But I strongly believe that if K-12 isn't compulsory, it really should be freely available to all (for those who cannot afford private options). Education shouldn't be a dividing line between haves and have-nots in this country -- we live in a country where hard work can lift someone out of poverty, and lack of access to education should never be allowed to prevent this.
Of course, if public education is bad (which it certainly is in many cities), that needs to be dealt with -- bad public schools will deprive the poor of access to an education as much as no public schools might. Some of the quotes you provide, of Dewey and others, suggest the problem with education is that it has become in thrall to bad educational philosophies. This is actually detailed in the E. D. Hirsch book I found the Jefferson quote in. Hirsch advocates a return to a basic "core curriculum", where students are expected to learn western civ and US history, as well as science, on top of the critical skills of reading, writing and mathematics.