This is one I'll play through two or three times so I'm not so worried about waiting on it.
Those timers, though, are needed. When there's no timer, the game gets noticeably easier. You can just turtle along and whatever aliens you find get blasted by overwatch shots before they can get into cover. If you do play with timers removed, you better up the difficulty to compensate. You might make a conscious effort to go easy on the Specialist class, too. They're even better at overwatching than the Support class of old so having no timers will give them a boost.