Reduce your input switching freq to say 10k or 100k and see if there are any more improvements. Start with a low switching freq and work your way up. This way you will be able to identify where your circuit limitations are.
Remember you are FM modulating the signal. By definition FM have a infinite number of sidebands although sidebands having levels less than 1% of the carrier level are ignored. Depending on the amount of deviation from the carrier (modulation index = freq deviation/mod freq) 1,2,3 etc. you can have (6,8,12 X mod freq) the required RF bandwidth
For example: If you have a mod freq of 5kHz with a freq deviation of 75kHz, the mod index will be 15. From Bessel functions table the required bandwidth will be 2 X 19(pairs of sidebands) = 38 X mod freq = 190kHz.
Pulse Modulation is used together with the "Vernitel" method to reduce overall bandwidth. In this method pulses AM modulate a subcarrier which then FM modulate the main carrier. The channel data is split into 2 signals high and low, each signal is transmitted over a seperate channel having a smaller total-bandwidth than the original data channel.