The energy produced by a nuclear fusion reaction for the impulse engines are readily quantifiable, and in Star Trek it did specifically say they were nuclear fusion reactors -- E=mc^2.
I'd say there's actually a simple solution for the problem.
In the uppermost and lowermost image of the first link, and the lower image in the second, and the third image all show some "unused" space in the saucer
The first and second image show this unused space to be located at the front and sides of deck 3, 4, and some of deck 7. There's also a gap on deck 5 where the saucer height is too high to house a deck but there is empty space there.
Granted the phasers occupy some of that space, but there's no evidence to suggest they're gigantic or take up a huge amount of space, so there's considerable volume within there for some fuel-tanks to be located.
The secondary hull definetly has some potential room at the very least on the upper most and lower most deck for fuel tanks to be located and fitted.