I'll bump you back up to the top with my 2 cents...
1) In some cases you can use grout to set tiles, but I'm not sure I'd want to do it on a shower floor. Someone else will be along soon to give a more definitive answer.
You could try what I used in my shower, after finding a pro here who uses the technique - grout the sheets of tile from the back before installing them, then set in thinset. You go back and fill in any holes in the grout the next day. My tiles were paper face-mounted so it was probably easier to hold the grout in that way, but I'm pretty sure the pics I saw here were mesh-mounted. (It was an all green-glass floor... I'll look for the post for you.)
2) What you described doesn't sound attractive. I'd cut the tiles to fit or adjust the layout.
Found the thread - see post #7: