When I implement progress bars I most often implement "pessimistic progress", so "considering all timeouts, worst case we are 46.5% (of the time) to some result", with an update every few hundreed milliseconds. As possible mix in data from completed subtasks.

Nobody ever complains if the process suddenly speeds up because progress was made before the timeout, as long as your initial estimate wasn't absurd (looks at Windows Explorer). Even a naive progress bar counting down the 60s timeout is more informative and satisfying to watch than an endless spinner.