To solve in a way that is more like HTA, add edges to the Starter Cube as shown below.

With the Starter Cube, in addition to half-twists for making setups, quarter-twists of the top and bottom faces and the center slice (horizontal) can also be used. That makes it possible to solve new configurations such as the following examples. The first cube below is solved with Sequence 3C-E2, the setup is made with a quarter-twist on the first move. The second cube is solved with Sequence 3C-E1, the first three moves make the setup with a quarter-twist on the second move.

The following configuration has a single misplaced facelet which can be solved by using Sequence 3C-E2 twice with setup moves between (quarter and half twists on moves 6 & 7) as shown on the first cube or with fewer moves using a new sequence as shown on the second cube.

The following configuration has two misplaced facelets (second one on left face), it can be solved by using Sequence 3C-E2 twice (with setup moves between) as shown on the first cube below. Another way to do it is with a slightly modified version of the sequence from the above cube as shown on the second cube below (second move is in opposite direction). If the two misplaced facelets on the slice are facing the wrong way then half-twist the left face (or the whole cube) to make the setup.

Each of the following cubes have two misplaced facelets (second on left face) which can be fixed as shown. A single misplaced facelet in any location on the horizontal slice can always be twisted to match one of the two setups.

This maneuver fixes four facelets with three moves.