I used the audio guide and skipped the towers, and I think I spent roughly 90 minutes in La Sagrada Familia. That included some wandering around and trying to get photos. The audio guide is briefer than most of those I encountered at Spanish churches (probably because they don't want people hanging around forever, crowding the church). Everyone is different in their level of interest, though; you might need less time, or more--plus whatever time required for the tower.
A fair amount of my 90 minutes was spent in the museum, not inside the church itself. There was no crowding at all in the museum, so I don't think it matters too much what time you get to the museum; that could be done after the tower visit in whole or in part. It would be nice to see the church at a less crowded time, if there is such a thing. I have no idea whether late afternoon would be better, crowd-wise, but the stained glass windows are lovely, and it would be a shame to visit too late in the day to appreciate them fully.
Since I didn't go up one of the towers, I don't know how far in advance of your ticketed time you must be at the tower. If you need to get to the tower 15 minutes before your appointment, 10 AM might be too early to schedule the tower; 10:30 AM might work well, assuming you do enter the church at 9 AM and are prepared to see the museum after the tower if necessary.