On the day you apply for British citizenship:
- you must have indefinite leave to remain in the UK, and
you must have been in the UK on a day exactly three years before the date of application.
You're allowed to have been outside the UK for up to 270 days in that three year period, and there's a degree of flexibility over absences exceeding that total, but there's no escaping the requirement that you must have been here three years ago, I'm afraid - nor the requirement that you have ILR.
So, I'm sorry, but there isn't a "fast-track" arrangement in place. But are you not able to get a national passport from your own country in order to visit your parents?