Hmmm... this thing is about twice as big as I'd estimated. Since you've declared your preference for gears and belts, which are both very serviceable approaches, your question then would be a matter of how to implement the design. Since Ank and I both suggested screwjacks, you might consider that as a good option. It's still technically 'gearing', since it's essentially a linear worm-and-roller train. Outside of hydraulics, it's my personal favourite where a lot of force is needed in a small package. Also, like hydraulics, the movement is non-reversible by the load; once you stop the drive motor, that thing is locked in position. With regular gears, chains, pulleys, belts, etc., you have to either maintain input power or build in an auxilliary locking device. It's particularly effective for situations like yours where the load is held at the end of a significant lever-arm. If it matters, it's also very smooth and quiet.