Tile – Shower Base over or to the side of tiles

• Step 1: Remove existing fixtures (toilet, sink, etc.)
• Step 2: Remove existing tile.
• Step 3: Determine if existing sub floor is appropriate for tile.
• Step 3 a: Replace existing sub floor (if necessary).
• Step 3 b: Install appropriate sub floor.
• Step 4: Install new tile.
• Step 5: Reinstall fixtures.
• Step 6: Enjoy your new bathroom for years to come.

This may not be the answer you are looking for, but to do the job right (in my opinion) you should start fresh.

If you don't feel comfortable doing the job yourself, you might think about hiring a professional.

I apologizes for the bluntness of my answer; as a home owner myself who has had to fix the messes others have created, in my opinion there is no excuse for not doing a job properly and (as Mike Holmes would say) making it right.

Removing the existing tile will cost you nothing but time, and in the end it will make you feel much better knowing that you can enjoy the remodel for years to come trouble free.

The usual approach is to cut them so that the offcuts are not so small - and NOT to try to keep an "uncut edge" anywhere.

So, you'd basically plan to burn 48" of tile on each wall, though you should be able to re-use some of the offcuts around the corner. No getting around the 1.75" ones on the back wall unless you want to get cute and put a 3.5" slice in the middle of two 8x16's to make the width. Whether that looks good to you or not is your call - if it does, consider the same approach on the side walls. Something like:

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and then on the longer sidewalls:

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Look OK is, of course, a highly variable and personal criteria. In your shoes I'd probably find that I could live with another wall tile, but I'm not you and you're not me.