I've finished the mortar bed, installed the vinyl liner and a new valve for the fixture.
In my crystal ball, I see a hammer in your future.
Is there any harm to putting an additional "insurance" liner under the Hardiebacker?
If you were led to believe that Hardibacker will provide you with any waterproofing at all, you have been seriously misled. While it will never be affected by the shower water, it will always be happy to allow water to go right through it. Showers need either a moisture barrier of 4 mil plastic sheeting or 15 lb roofing felt installed over the framing and overlapping the liner prior to installing the cbu or, a surface waterproofing membrane can be applied to the cbu prior to installing the tile.
I also have some DAP (3.0) Waterproof Caulk I was going to use on the backer board joints prior to affixing the alkali-resistant tape.
Just thinset and tape them. Your moisture barrier or your surface waterproofing will take care of water issues. You do use caulk where the tile meets tile at the wall intersections though.
Let's backtrack though. Shower construction goes sloped mud bed, then liner, then moisture barrier, lath for the curb (no cement board on the curb), then install the cement board with no fasteners in the lower 8 inches, then your settng bed of mud to lock in the lath for the curb and the lower portion of the cement board to the shower framing.
Is there any down side to taking these extra steps?
The thickness of the liner in the corners will cause your walls to be out of plane and make for bad looking corners, especially with a pattern or diagonal install or large format tile install.
Did you build a bench in this shower?