Here is a solution that works with Spannable, with the cavate that if the right and left are too wide, they will overlap on the same line. Since to do the Left/Right trick with a spannable requires a line feed between Left and Right, my fix is to add a spannable that reduces the line height to zero (i.e. overlapped lines) for the one linefeed and then restore normal line height after that.
    String fullText = leftText + "\n " + rightText;     // only works if  linefeed between them! "\n ";
    int fullTextLength = fullText.length();
    int leftEnd = leftText.length();
    int rightTextLength = rightText.length();
    final SpannableString s = new SpannableString(fullText);
    AlignmentSpan alignmentSpan = new AlignmentSpan.Standard(Layout.Alignment.ALIGN_OPPOSITE);
    s.setSpan(alignmentSpan, leftEnd, fullTextLength, Spannable.SPAN_EXCLUSIVE_EXCLUSIVE);
    s.setSpan(new SetLineOverlap(true), 1, fullTextLength-2, Spannable.SPAN_EXCLUSIVE_EXCLUSIVE);
    s.setSpan(new SetLineOverlap(false), fullTextLength-1, fullTextLength, Spannable.SPAN_EXCLUSIVE_EXCLUSIVE);
And we have the small routine to handle the overlapping lines:
    private static class SetLineOverlap implements LineHeightSpan {
    private int originalBottom = 15;        // init value ignored
    private int originalDescent = 13;       // init value ignored
    private Boolean overlap;                // saved state
    private Boolean overlapSaved = false;   // ensure saved values only happen once
    SetLineOverlap(Boolean overlap) {
        this.overlap = overlap;
    }
    @Override
    public void chooseHeight(CharSequence text, int start, int end, int spanstartv, int v,
                             Paint.FontMetricsInt fm) {
        if (overlap) {
            if (!overlapSaved) {
                originalBottom = fm.bottom;
                originalDescent = fm.descent;
                overlapSaved = true;
            }
            fm.bottom += fm.top;
            fm.descent += fm.top;
        } else {
            // restore saved values
            fm.bottom = originalBottom;
            fm.descent = originalDescent;
            overlapSaved = false;
        }
    }
}