Metric is quite hard but I would suggest having more than 10 timeouts per print should show the modal and inform the user as soon as the threshold is reached with a simply modal window in the browser and whatever solution fits on the display.
Maybe it would also help to have an (optional) summary at the end of printing (or extend the already existing message) and give infos like duration, length filament used errors during print, so no on the fly warning would be necessary.
My idea was not giving exact solutions to the problem but letting the user know that there are many timeouts which could (and probably would) affect the print quality. As I said, at first I thought of a hardware defect and then realized that there were so many timeouts. It was the last place I assumed there could be a problem.