using URL shortener from google sheets with long url

Question

Can anyone tell me how to use bit.ly (or any other url shortener) with a very long URL with a google sheets script.

The code I have is

function bitlyGroupId(accessToken) {
  var headers = {'Authorization' : 'Bearer '+accessToken};
  var params = {'headers' : headers};
  var fetchUrl = 'https://api-ssl.bitly.com/v4/groups';
  var response = UrlFetchApp.fetch(fetchUrl, params);
  var group_guid = JSON.parse(response.getContentText()).groups[0].guid;
  return group_guid
}

function bitlyShorten(longUrl) {
  var accessToken = "<TOKEN>";
  var group_guid = bitlyGroupId(accessToken); 
  var fetchUrl = 'https://api-ssl.bitly.com/v4/shorten';
  var headers = {
    'Authorization': 'Bearer '+ accessToken,
    'Content-Type': 'application/json',
  };
  var payload = {
    'group_guid' : group_guid,
    'long_url' : longUrl
  };
  var params = {
    'method' : 'post',
    'headers' : headers,
    'payload' : JSON.stringify(payload),
    'muteHttpExceptions' : false
  };
  var response = UrlFetchApp.fetch(fetchUrl, params);
  var shortUrl = JSON.parse(response.getContentText()).link;
  return shortUrl;
}

This works well for shorter URLs but when I have a long URL (over 2k chars) i get the error INVALID_ARG_LONG_URL.

Does anyone know how to get this working?