You can get inner tubes which are not circular, just closed sausages of rubber with a valve in the side. You can fit and remove them without removing the wheel.
You should also fit the toughest tyre you can find such as Marathon Plus.
The problem with fitting 2 inner tubes is that whatever made the puncture is probably still embedded in the tyre and will cause a 2nd flat.
I have an Alfine hub gear but it uses disc rather than drum brakes so removing the rear wheel is not so difficult. I figured out how to separate the cable from the cassette arm. The cable has a nut to engage with a slot in the cassette arm. You slacken off the cassette arm using a very small allen key in the appropriate hole (which they tell you about) but then you have to put a little rotation into the nut to slide out of the cassette arm easily.