I don't believe plaster of any kind would be good to use for what your planning. Plaster needs something better to adhere to than a smooth surface. What you could use is a small premixed container of patching cement. Being applied to the Hardie board is very similar to applying it to existing concrete. Although you should also use a bottle of acrylic primer on the Hardie board as you apply the patching cement. Both of these products are available at home improvement stores.
Now if you feel you would still like to use plaster you could make it work by first applying a wire backer to the Hardie board. Something like chicken wire would work. It would be tacked in about every foot and in the corners. Staples won't work too well on this type of hard board but you could use small nails with heads like a roofing nail and place the nail at each location in a corner of the wire. This would probably work but if I were doing this myself I'd go for the patching cement.
As for your other thought of taking out what you have done and then re-installing to have the area come to a depth that you could just use regular "thin set" for tile. The Hardie board finish surface which is not real smooth would make an ideal surface for thin set to adhere to. So if you don't mind the tear out and re-do this would be the best choice of all three.
Dennis (cut2it)
C&onstructi&on C&onsultant
Over 40 yrs. as General Contractor for new const. & remodel - retired with time for you.