Okay, folks, here's the workaround for the double-press cursor in TextMaker HD.
Go Tools/Customize/Keyboard Mappings
With Default highlighted, click Edit
Under Group, go to Editing
In Editing, under Command, click on "Character left"
In the Shortcut box ("Please press accelerator"), I chose Ctrl+Left (Control with left arrow)
Hit OK
Then hit Apply
There are also keyboard mappings available for Line up, Line down, and Character right.
I chose Control for the accelerator since my Alt key is already heavily keystroked and the Control key (at least on the US keyboard) is easily found (furthest left key on the fifth row).
[I have not yet figured out how to make the keystroke repeat when by holding it down. EDIT: it seems to be an issue with Control as choice of accelerator. If Alt is chosen instead, there is repeat upon holding down keystroke]
Thank you, kc853, for pointing us in the right direction, and I hope you find a solution to your backspace issue.
Jake