Alternative ways to step up voltage?
If the cell input impedance is more or less a large capacitance, your first job is to make it look resistive. This makes the drive amplifier easier to specify and design.

Design a lowpass LC ladder filter with an infinite output impedance (good filter design tools will let you choose one port with zero and infinite impedances, as well as a finite impedance). This infinite Z port will have a shunt capacitor there. Design the filter bandwidth to cover at least your operating range, and the filter impedance so that this final C is as large or larger than the C of your load. Now 'absorb' the load C into the filter C by reducing the filter C by the load capacitance.

Now have another crack at amplifiers. There are some quite impressive video amplifiers and fast opamps around. With a resistive load to drive, you'll find that RF transformers behave better as well.