Sorry for the late reply.
Let's recap: the problem is that during set-up everything works correctly and focus responds to the <<<, <<, < / >, >>, >>> buttons properly, but when shooting the stack not all focus adjustments are being made properly, is that a correct description of the issue?
Take your camera and turn live view on (without remote control, just regular hand-held operation). Press the AF button to access the list of focus modes, scroll through the modes with the wheel controller. Select the "One-Shot AF" mode.
Now, while still in live view, change the AF zone pattern. Try every single option to see which one works properly with Helicon Remote. Refer to page 121 of
this user manual PDF file for instructions on how to change the AF zone.
Also, before you do all that make sure your camera is set to photography live view mode, not movie mode. If it was in movie that could be why it doesn't work.