When you worked on the BB you must have had the rear wheel off? I struggled with a creek for a while, a while ago. It sounded like it was coming from the bottom bracket. I disassemble, assembled to no avail. It ended up being the rear QR. I put a little grease on the threads and drop outs tightened and solved.
Your play issue may really point to the BB, but it does seem every noise comes from the BB regardless of where it really is.