If the assignment question has the proper behavior for your task, we shall start with that. However, I am not sure, if you'll not be limited by having only one word (instead of two) in that question type.
Visual edits (font size, positions) can usually be done via CSS. So, if you have a question that does the right thing, you can post a prestest URL, and we can help out with some CSS.
> or from scratch
That will require a lot of JavaScript learning. Not the easiest way, probably.
> The original design of this question is similar to polarity profile with two options, but I can't replace those checkboxes for "=" and "<>".
The scales would have a card layout one could enable, but not the polarity profile...
However, Writing some JavaScript to do that would be much easiert than writing a new question type. The disadvantage of the polarity profile is, that you will have to go from page to page (which can be automated but still triggers loading time) between the items.
So ... with what question type would you like to start?