How to increase frequency modulation index?
It seems an absolute pull range of a VCXO will limit the modulation
  index. Is there possibly a way to extend it?


You could use a colpitts oscillator and varactor - you could "wrap" around it a PLL so that centre-frequency stability is as good as a reference crystal. I've done this a few times on applications ranging from 80 MHz to 400 MHz and got FM deviations of +/- 5MHz no problem and data rates of up to 15 MBpsec.

EDIT

Here's a PLL that takes 6mA and works upto centre frequencies of 400MHz: -



You need a small MCU for setting up the division ratio to make lock plus a simple varactor controlled colpitts will do the trick. Or, try the LTC 6905: -



I particularly like this device because it's really simple and doesn't go belly-up on large G-forces (unlike cheap xtals)