It does not appear that I am going to be able to earn the droids or the additional level before time runs out on Service to the Empire. Will I still be able to obtain these through playing the game normally?
I hate to be the bearer of bad news but I don't think you'll be able to earn the limited edition rewards (3 droids + Imperial Marches level) in normal play, unless the devs change their mind.
The limited edition rewards from the Christmas event prior (Holiday Special Boba Fett and Panna City Medicines level) were not made available in normal play. So I reckon this will be the same.
I'm trying out the rollback method as well and I should note three things:
1) Today I got an alert that it was my last day to complete the event, despite my timer having a full week left. So don't get your hopes up.
2) It's really important to turn the application updates off so that a patch update doesn't throw a wrench in your gears while you're trying to trick the game.
3) make sure you have absolutely zero pending orders or tasks in the game when you roll back because a 3 minute order will turn into how ever many days you roll back.
ETA: Because my phone had access to wifi, it updated anyway, haha. Sorry, but it looks like you can't trick the game at all unless you make sure there's no way it can connect or update.
There is a way. It's cheating. But, I believe if you turn off your wifi (and possibly cellular connection) and set your clock back by a few days, you will be able to keep going. When you properly reset it, you will lose a bitizen out the airlock, though.
I haven't tested this, but given that the game times off of the local time in your phone, this will probably work.