Hi Damon,

May 12th, 2022 — For future people to read.
On this date dropdown values for the request pages are not stored in the DOM, because of that, it's only possible to delete the values when someone clicks the dropdown.

Solution
Here is the clean solution. Please remove all the code (you added) from your current sample.
It is Vanilla JS, jQuery free and not guestimating when elements are added to the DOM (no setIntervals).

I verified that this works and added comments in the code below, what each step does.

Don't forget to replace the form ID on this line.

// function that waits for the element to be added to the DOM.
function waitForElm(selector) {
    return new Promise(resolve => {
        if (document.querySelector(selector)) {
            return resolve(document.querySelector(selector));
        }

        const observer = new MutationObserver(mutations => {
            if (document.querySelector(selector)) {
                resolve(document.querySelector(selector));
                observer.disconnect();
            }
        });

        observer.observe(document.body, {
            childList: true,
            subtree: true
        });
    });
}

// native JS way of waiting for the DOM to be ready
document.addEventListener('DOMContentLoaded', function() {
  // Only run this code on the new requests pages
 if (window.location.href.indexOf("/requests/new") > -1) {
   
  // now let's actually wait for the element to be added to the DOM
  waitForElm('.request_ticket_form_id .nesty-input').then((elm) => {
    // the elements are now added so we can start binding the deletion whenever the click happens
    document.querySelectorAll('.request_ticket_form_id .nesty-input').forEach((el) => {
      // now we can bind whenever someone clicks on the form input, to delete one of the forms
      // but only do this when the user is not part of organization
      // in this example the next line checks for the organization with name: Managers
      var isPartOfOrg = HelpCenter.user.organizations.find(o => o.name === 'Managers');
      if (!isPartOfOrg) {
          // replace the ID here with your Form ID
          el.onclick = () => document.getElementById('6092785826321').remove();
      }
    })
    });
 }
}