With phrases like you fear "gaming the system", I presume you worry a student may skip something that is essential, but maybe can't be worth a ton of points?
If may be possible to declare a question a "required field", just like many forms do. So even if it's only worth 10 points, and the student has decided they'd be happy with a B or C, if you want to be SURE that a student can (for example) definitely demonstrate they know which example shows plagiarism vs correct citation, then I'd mark that question REQUIRED.
examples of various similar strategies over a whole semester...
I used to do a similar thing in my English classes. The research paper itself was "only" worth 20% of the grade, but my syllabus and assignment sheets made it clear that a non-passing grade on the research paper would mean the class requirements were NOT met, and it was an automatic failure. Basically it was a GATE, not merely a quantity.
Other profs in my department had similar "gated" systems. In order to achieve a C, a baseline level of requirements must be met. In order to achieve a B, those had to be met AND the next level of requirements. An A required all of the things. This was to prevent people who were "naturally good writers" from skipping over the process and class-interactions.
BlackBoard (our LMS) allowed assignments to be hidden unless the student had achieved other dependent requirements, and I think there were a few Econ professors who used that to good effect -- you had to score X on a comprehension test to open up the assignment details. You had to have submitted a draft before the link to submit the final would open up.
If parts of your exams are mini-essays or paragraphs, make sure you have a clear rubric - a guided checklist of what you want. This helps you focus on the content (were all terms used accurately? Did they give the key exception?) and not get distracted by good or bad style.
Back to your exam: Discuss with others in your department about the norms and expectations, but feel free to explore alternate formats besides pure numerical, as long as they are fully disclosed. Set students up to succeed, but make sure that you're also getting the proof you need as an instructor to indicate sufficient mastery.