I feel it would be convenient to make theme changing faster

just a heads up, instead of document.location= you should use location.assign()

Here's a full script to add the form to the bottom of the page like when you're signed out:

(function() {
  const storage_key = "theme-options";
  const max_cache_age = 60 * 60 * 1000; // One hour

  const get_form = () => {
    return new Promise((resolve, reject) => {
      let now = (new Date()).getTime();
      let options = window.localStorage.getItem(storage_key);
      options = options && JSON.parse(options);

      // If the cache is up to date, use it.
      if (options && (now - options.timestamp) < max_cache_age) {
        resolve(options.theme_select);
        return;
      }

      fetch("/settings")
        .then(resp => resp.text())
        .then(html => {
          let parser = new DOMParser();
          let doc = parser.parseFromString(html, "text/html");
          let theme_select = doc.querySelector("#theme").outerHTML;
          let option_data = {
            timestamp: now,
            theme_select: theme_select
          };

          window.localStorage.setItem(storage_key, JSON.stringify(option_data));

          resolve(theme_select);
        })
        .catch(reject);
    });
  };

  // Ripped from tildes.js
  const apply_theme = function(event) {
    event.preventDefault();

    // hide any IC change message
    $(this).parent().find('.form-status').hide();

    var new_theme = $(this).val();
    var selected_text = $(this).find('option:selected').text();
    var $setDefaultButton = $('#button-set-default-theme');

    // persist the new theme for the user in their cookie
    document.cookie = 'theme=' + new_theme + ';' +
      'path=/;max-age=315360000;secure';

    // remove any theme classes currently on the body
    $body = $('body').first();
    var bodyClasses = $body[0].className.split(' ');
    for (i = 0; i < bodyClasses.length; i++) {
      cls = bodyClasses[i];
      if (cls.indexOf('theme-') === 0) {
        $body.removeClass(cls);
      }
    }

    // add the class for the new theme to the body
    $body.addClass('theme-' + new_theme);

    // set visibility of 'Set as account default' button
    if (selected_text.indexOf('account default') === -1) {
      $setDefaultButton.removeClass('d-none');
    } else {
      $setDefaultButton.addClass('d-none');
    }
  };

  const insert_menu = () => {
    get_form().then(theme_select => {
      let footer = document.querySelector('#site-footer');
      let themeForm = document.createElement("div");
      themeForm.innerHTML = `<label for="theme">Theme:</label> ${theme_select}`;
      themeForm.className = "site-footer-theme-selection";

      footer.insertBefore(themeForm, footer.firstChild);

      $('#theme').change(apply_theme);
    });
  };

  insert_menu();
})();

I don't know how to make it work with greasemonkey, but if someone wants to do that we'd have a complete solution.

Edit: Maybe someone can add this to the "Tildes Extended" extension.