not an answer only disagree with, my comments against, no reviews, not tried your code, apologize me that there are any reason, maybe my bad
doInBackground() is bridge between AWT/Swing EDT and Workers Thread(s), by default never notified EDT
process, publish, setProgress and done() notify EDT
then Swing Timer inside doInBackground() is against all intentions, why was SwingWorker implemented in official APIs, there is place to execute long running, hard or non_safe code
again SwingWorker is designated as bridge between AWT/Swing and Workers Thread(s)
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there are two ways
use CountDownLatch with invokeLater() or Swing Timer. don't mix that together nor from SwingWorker
use CountDownLatch, util.Timer, SheduledExecutor with notify EDT by wrap (only relevant, only output, methods will be repainted on the screen) Swing methods to the invokeLater()
use only Swing Timer (non_accurate on hour period)