[Mondial]

It does seem the capacitance of the Philco trimmer is quite low, but if you notice the secondary coil has a lot more turns than the primary and as such will need a smaller resonating cap. 

My feeling that you may need lower capacitance is based on your observation that you had the greatest output from the secondary when the trimmer screw was backed out all the way, corresponding to minimum capacitance. Since you never achieved a definite peak, it is possible that even lower than the minimum trimmer capacitance is necessary to bring the secondary into resonance.

My guess is that the trimmer cap plates could have lost some of their springiness and therefore are unable to increase the spacing between them enough when the screw is fully loosened.