The test was done under full working load (see below). The seating position can be judged from the following composite picture which shows the cranks fully extended towards the body, and also away from the body (the seat is a wooden block). Instead of handgrips, a pair of LOOK pedals was used, which are nicely rounded and easy to grip:
Note that the angle is upwards, with the major axis of the ellipse oriented more or less towards the belt of the rider. This may not be the best arrangement for all persons, but after trying different angles the author found this one to be the best. When working the pedals, the torso moves in a kind of rocking motion (there was no backrest in this setup), with the shoulders also contributing very much. One reason for choosing this particular angle was the ease with which one can maintain a smooth motion through the "dead spot" at the start and end of the ellipse: With the long axis horizontal this felt less smooth. Further, this way it is possible to be seated very close to the cranks, which may be an advantage.
Lastly, there may be advantages (or disadvantages!) to this arrangement with respect to the other hand operated controls. Steering may be better with elliptical cranks. If brake and gear levers are attached to the handgrips, the elliptical motion may simplify routing of the cables. These are matters for experimentation!
The equipment that was used in the animations above consists of a stationary test bed. The load was provided by mounting a conventional 18t freewheel on the driveshaft of a spray-painting air compressor which is normally powered by a 1hp electric motor. Here the motor is actually being driven by hand! With suitable gearing it was possible to operate it at a realistic "road speed" while driving the compressor. Some details are visible in the picture below. Note that the chain is crossed, so that tension is taken from the bottom of the chainwheel to the top of the 18t freewheel, while the slack return side of the chain is at the top. This was only required because the freewheel could only be mounted in one way onto the motor.
An intriguing possibility is to use this as a kind of ergometer: Connect a small tank with pressure guage to the compressor, and fit a heart-rate monitor to the person doing the work. Now you can measure how long it takes to achieve a given target air pressure, and relate that to the resulting heart rate. When you change something like the length of the cranks, you can see if that requires more or less effort to achieve the same air pressure in the same time.