Using rounded values, let's run thru a few calculations. The dimensions of the pneumatic spring:
overall volume 2.2 cu.in.
bore .93 (.18 valve stem)
cross sectional area .65 sq.in.
During the pump stroke, the pressure in the reservoir rises from 925 (the precharged value) to 1000. The displacer piston is moved .28 in. in the process of forcing in the ~12 cu.in. of air. During firing, and assuming adiabatic expansion, the reservoir pressure drops to 895. So......the force exerted on the piston, from start to finish goes from 650 lb (1000 x .65) to 582 (895 x .65). The effective spring rate, K (change in force/change in length), for this configuration is 245 lb/in. Since maintaining high cycle pressure is our goal, K should be kept small.
What can be accomplished with a mechanical spring within the same geometric outline? From a Schnorr catalog, #009100 fits our requirements of max force and OD. Listed values of 660 lb @.016 deflection and initial height .081 will work. The length of space available, after the pump stroke, is 3.12 in. and 48 springs [3.12/(.081-.016)] will fill it. Assuming a linear relationship between force and deflection, the spring rate for such a stack would be 840 and the generated pressure would go from 1000 to 640.
Comparing average cycle pressures for the first part of the overall expansion process........950 vs 820. The spring stack would weigh .8 lb and cost upward of $50. Hope this helps.