RTF is a rather old format (not updated since 2007). Being a M$ format, even if specs are released, the usage frequently differs from what the book says. As a consequence it is difficult to write reliable input/output filters. You’d better ask if another format is possible.
Also, LO 126.96.36.199 is outdated. Try with a more recent version (current stable is 188.8.131.52) to see if the RTF output filter has improved.
Last question; “left aligned text above and below it” are in separate paragraphs? Having different alignments in the same paragraph is already tricky in native format and I don’t think it translates correctly to RTF.