Mortar supports millions of tubs around the world...why wouldn't it work for yours? It doesn't need 100% coverage. Many people put down a bunch of piles, then push the tub into them, ensuring it is sitting level in all directions. If you install your ledger board(s) well, you can use them as a guide and push the tub down into the mortar until it touches the ledgers, then leave it alone until the mortar cures at least overnight.
The lip, or deck of most tubs is required to be supported by ledger boards. Most tubs are NOT designed to actually hang from the ledger boards, but only to prevent them from moving when, say, someone sits on the edge. They also prevent the tub from tipping.
SOme people put some plastic on both the floor and on top of the mortar so it's easier to remove the tub eventually and to prevent the floor from sucking out the moisture from the mortar. Mortar cures, it doesn't dry, and if it loses too much water by drying, it won't be as strong.