Perhaps you can put a different seat back in your kayak. I had a Wilderness Systems Pungo with an excellent seat, just as an example. Some back bands are ratcheting or otherwise adjustable and can be placed firmly against the lower back. If your kayak is plastic, it's a simple matter to drill attachments for a new seatback.

If you decide to go with a canoe, you can also get a supportive seat back for that. I have, and it eliminates my lower back pain.