The first two choices are easy. Just use a randomizer to display them.
Similarly, the last four are also easy. Display all 10, add display logic to each choice and hide it if it has been displayed earlier.
For the middle 4, one option would be to use Loop and Merge, Loop of the first question and use only the Not Displayed Choices. Then randomize to show only 4 choices.

Thanks so much, ahmedA! This seems quite promising!
I'm just a little confused about how to implement your suggestion for the middle 4.
If I understand correctly, for the first block, you recommend using block-level question randomization like this:
For the last block, you recommend duplicating the questions and doing this:
For the middle 4, I'm not totally sure what you mean you say: "use Loop and Merge, Loop of the first question and use only the Not Displayed Choices. Then randomize to show only 4 choices."
I think you're suggesting something like the following, using the "Loop Based Off of a Question" option from the Loop & Merge menu, but that only works for displaying question ANSWERS, not the questions themselves. Perhaps I set up the first block incorrectly?

Any guidance?
Thanks again!

Step 1: Create a question with 10 choices (V1-V10). Your vignettes will be your choices. Randomize the choices to show only 2. Hide this question using JS. Add the following to the question:
Qualtrics.SurveyEngine.addOnReady(function () {
    this.questionContainer.hide();
});

Step 2: Create a block with all your 10 questions. To each question add display logic to show only if the corresponding vignette was displayed. For example, show vignette 3 if V3 was displayed and so on.
Step 4: Create a loop and merge block and loop of not displayed choices of the question in step 1 and show only 4.
Step 5: Copy the block in step 2. All questions and the display logic. Add another display logic to each question to not display if the corresponding vignette was displayed in the loop and merge block.

This was (a) wildly counterintuitive, (b) so much harder to accomplish than it ought to be, but (c) so, SO clever. Wow, ahmedA!! Thank you for taking the time and for such a clear description of the solution--walking me through carefully step-by-step. Amazing. Thanks!