Must I ... slink off without being able to bring to share my thoughts?
The best way to share your thoughts on these sites would be to find relevant questions and answer them.
After you feel you integrate well with the community and understand what is acceptable and what isn't, you might venture into asking questions regarding your particular interests in math.
However, as you discovered quite abruptly, many of the existing users don't believe that your questions fit the site guidelines. One of the reasons is likely that your questions are very subjective - there is no single correct answer that can be objectively viewed by all and understood to be correct.
Further, your questions are not about math and math problems - they are about education and math understanding. They really don't fit the site's charter.
You might consider supporting the education specific site http://area51.stackexchange.com/proposals/23685/educators or supporting a math education specific site at http://area51.stackexchange.com/proposals/35226/mathematics-teacher-educators
Neither of them are ready for questions or answer yet, but they seem to be the best place for your questions.
But even in those sites you need to be careful to understand both the site charter, and the community. You can jump in with both feet, but a careful study of the community might help you avoid the same situation you found at the math site.
To answer your main question, "Could I have avoided being suspended..." The answer is yes - you could have answered questions primarily, read existing questions and answer to understand the community's expectations, and test the waters with only a question or two to see how the community reacts rather than starting right in and beginning several questions without a good understanding of the community.