Is your homeschool transcript just grades and numbers? If that is all you have for your application, most schools are going to require more numbers - the standardized test scores. My daughter went to (but did not graduate from) an expeditionary learning school. No grades, but each student produced a portfolio of work each year. Some schools were more interested in these portfolios than in gpa’s (since there weren’t any) and standardized test score. All students had at least an ACT score since that test is taken by all 11th graders as a NCLB exam.
There are other ways to get into private schools than standardized tests, but you have to do the legwork, you have to find who wants you. The easy way is to take the test. And you’ll have to find how to pay for it since some schools award their merit money based on test scores.