Efficiency and focus is the name of the game in Imperial Assault. Let's look at your specific issues:
Running out of time
My group ran into a similar issue until we realized that many of the missions in Imperial Assault are not designed to be completed by "clearing the dungeon". Instead, we had to pay careful attention to the specific mission objectives and focus on the most efficient way to do that, often completely ignoring many of the enemies. This may help your players as well, and as the Imperial player (basically the Game Master in classical RPG terms) you can assist them by reminding them of what is important before and during the mission.
Too many enemies to deal with
Similar to the time issue, the answer to this is to pick-and-choose what is worth fighting and what isn't. Unlike Descent 2E (another FFG tactical miniatures game), you can move through enemy figures in Imperial Assault, meaning it's almost impossible for them to completely block you from reaching an objective. Some figures are truly too dangerous to leave alive, while some are mostly just a nuisance that can be ignored (and potentially left behind if your team moves fast enough across the board).
Rebel characters not able to pump out enough damage
For those times when you need to pump out damage, coordinated fire can be very important to completely eliminate a target in one round (instead of just damaging several separate targets). It is also important to note that status effects can be more powerful than any amount of damage: an immobilized melee character with no targets within reach is a non-entity, and a 1-hit immobilize can be much easier to achieve than a 1-shot kill. Similarly a stunned ranged character with no targets in line-of-sight is also negated for a full round, since they cannot move-and-shoot that round.
One final note I will offer is that not all heroes are created equal. By comparison to each other, some specific heroes are really great in any situation, other heroes are bottom-of-the-list no matter what situation you set up for them, and a lot are hanging out in the middle. Ranged characters tend to have an advantage in efficiency over melee because they have much more flexibility in where they can position themselves. Your Rebel players may need to accept a compromise to "I want to be a Jedi" in the name of effectiveness.