While the 3-color solving method shown on this web-site was developed independently and is very different from HTA there are some obvious similarities in that both start by solving as a 3-color cube and both finish by reaching a configuration that can be solved with half-twists. The 3-Color Cube method can be modified to work a bit more like HTA by doing the following.

After solving the corners on two opposite faces using the Starter Sequences, instead of solving the corners on the remaining faces, solve the edges on the two faces with the solved corners using the 3-Color Edge Sequences and some additional ones here. Try solving random Starter Edge Cubes here.

After solving all of the corners & edges on two opposite faces (as 3-color), solve the remaining corners using the instructions here. The 6-color corners can be solved before or after the remaining 3-color edges are solved, however, there are some differences at this stage with this method (see Solving Notes at bottom of page for more details). Complete the solve using the instructions for 6-color edges.

An advantage of this method is that after solving the corners & edges on two opposite faces (as 3-color cube) the setups for the 3-color edge sequences can always be matched exactly when solving the rest of the cube, no need to make partial matches where only some of the misplaced facelets get fixed. Another advantage is that the case in which no misplaced facelets can be fixed is avoided. Disadvantages are that it requires more sequences and adds additional complexity to the 6-color corner solving stage as described in the section below.

Solving Notes:
If solving 6-color corners prior to 3-color edges and the parallel sequence is needed then make the setup such that the solved faces are on the left and right, otherwise two of the solved edges will get misplaced. If the waterwheel sequence is needed and the pair of faces where corners can be solved with half-twists (as 6-color) is not the same pair with solved edges (example here) then one of the solved edges will get misplaced, fix it after applying the sequence (with sequence 3C-E2). If solving the 3-color edges first, then some edges will get misplaced with either of the 6-color corner sequences but that is also true for the 3-color solving method as described here and here.