Another way to convert steam to mechanical force is a simple piston. take a look at the Air Hammer shown here:
Simple Air Hammer this is a system using a simple piston and air pressure to move a large weight up and down at a high rate of speed. You could simply attach the piston to a crank and gear it to the speed needed. The size of your piston is determined by the amount (CFM) of steam you can generate.
The Airdrill / die grinder CFM problem is that the CFM rating is what is required to turn that tool at the rated RPM. The PSI determines the amount of torque it will have at that rpm. If you double the psi and half the cfm you will just slow the tool down because it will now be "Starved" for air. Basically you have an internal cavity within the tool that must be filled. PSI is the amount of pressure you are filling it with but with out enough volume the cavity cannot fill fast enough because the tool is using that air as it comes in. As air enters the tool the tool begins to rotate and air leaves the tool, if the tool does not have enough volume it can not fill the cavity fast enough and therefor can not efficiently harness the pressure of the air to apply it to the rotational load before the tool rotates the air out.
In a simple piston setup like the air hammer uses if you have a lower volume it will simply move slower as the valve to switch to the opposite direction is activated by the position of the piston. Here the PSI will determine the power the piston pushes with but the volume determines the speed it moves at. These hammers regularly swing a 25-250# hammer at 250 beats per min which would give you a 250 rpm crankshaft. If you increased the hose and connector size you could increase the speed but these types of systems are meant to run slow and produce a tremendous amount of torque.
A hydraulic piston will work but you will want to include some type of lubricating fluid and will want to keep an eye on the seals of the piston as the heat may break them down. You can find steam pistons on the web but you can find hydraulic pistons at your local farm supply store.
Gearing can be done using pulleys and belts or bicycle chains and sprockets, but if you want it to last for a while I would look into something along the lines of a go-kart drive train with jack-shaft and pulleys.
The turbine you are drawing looks fun to play with but the pressure / volume required to run it would be FAR more than that required to run a piston or air tool setup.
If your Die Grinder could not generate enough torque to run it, try wrapping a short belt around it and the alternator. The die Grinder should rotate at about 10k rpm so cutting that down to even 10:1 (the socket on the die grinder diameter=1/10 the pulley diameter) would still give you 1000 rpm on the alternator and you will have a increase in torque of ~*10.
As for ease of build, I think I would not give up on the air tool side of it just yet. Perhaps instead of using a belt, use a drum sander adapter for the grinder. This could be placed against the pulley directly rotating it, start off slow so you don't just burn the adapter up but it would work about the same as a Tire Hammer which is an alternative to the air hammer
can you tell I like hammers?