Putting the injection in on the opposite side will have a poorer success rate. Typically, a large volume transforaminal injection on the same side would yield the best success rate (TFESI) without the risk of a dural leak. You might be surprised how effective it is.
Donald Corenman, MD, DC is a highly-regarded spine surgeon, considered an expert in the area of neck and back pain. Trained as both a Medical Doctor and Doctor of Chiropractic, Dr. Corenman earned academic appointments as Clinical Assistant Professor and Assistant Professor of Orthopaedic Surgery at the University of Colorado Health Sciences Center, and his research on spine surgery and rehabilitation has resulted in the publication of multiple peer-reviewed articles and two books.