Manual Vectorization for Large Prints

I need the hand-drawn artwork in “image-to-redo.jpg” rebuilt as a clean, simple vector because every auto-trace attempt leaves rough edges that will show once the piece is enlarged for a large-format print... (Budget: $30 - $250 USD, Jobs: Adobe Illustrator, Digital Art, Graphic Design, Illustration, Illustrator, Print Design, Vector Design, Vectorization)