Would something like this work?

• Put all 50 items as individual response options in a multiple choice question.
  • Use the “edit multiple” feature to copy / paste all of the items into the question in bulk.
  •  Put the question on its own page.
  • Hide the question from respondents using Javascript, so that the question not display. Make sure you DO NOT make the question required, or it’ll get glitch-y. Javascript to hide the question would be something like this (from this support post):

Qualtrics.SurveyEngine.addOnload(function() {
    jQuery("#"+this.questionId).hide();
    this.clickNextButton();
});

• Add another block. Click on the block so the “Edit block” pane appears on the left hand side of your screen. Make the block a “Loop & merge.” 
  • Click the button to turn on the loop and merge. Check the box to loop based off a question. Select the hidden question you just made, and make the logic show the loop if the item was *displayed.*. Unless you add randomization or display logic to your hidden question, all of the items should count as “displayed” (even though you had that Javascript to hide the question)

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  • You can randomize the loop order from here, too. You can also display a random subset of the loops if you don’t want respondents answering for all 50 items (which sounds like it could take a long time)
  • Put your matrix question into this loop & merge block. Add piped text for the Loop & Merge field so the matrix question is referencing the correct field each time. Most likely, you’ll use something like ${lm://Field/1} but you might also want to add other fields to your loop & merge settings and use one of those. It just depends on your specific data/use case.

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Thank you for your response @lizb311. I’m just getting back to this project now. I’ll try your suggestion and see if I can make it work. I may check back in if I have any questions.