Is there a way to generate 10.7 MHz from any of these above frequencies _without_ using a PLL?
Sure :
The modern way would be a Schmitt XOR gate, and simple third phase RC delays. Then (A XOR C) XOR B gives 3f ( eg using SN74HCS86)
or, you can make a ringing circuit with an LC and moderate Q at 3f, with Schmitt follower, and kick it with a narrow impulse at f.
These give 3.574595 *3 = 10.723785 MHz