If $(document).ready() too early, you can use $(window).load(...) . This is indeed at the end of the process, but I cannot come up with anything in between.
If you can check the placement, you can start the survey with $(document).ready() and wait for the placement to match what you expect, or stop changing, or some. Polling every 10 ms or so will not have a noticeable effect and may allow you to get rid of the counter earlier than the load event.
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