Should I ground my solar installation using the same ground spike I use to ground my Amateur radios? If lighning strikes the solar panels, won't the strike run down to the spike and then back to my radios?

Are you certain the current ground rod is good, according to code? If lightning strikes it follows the least resistance which is to ground, not your radio.

I agree with ballengerb1 - if the ground rod is properly installed based on the type of soil you have there should be no concerns. However, be sure to double check the grounding instructions for both your amateur radio installation (I assume you mean grounding for the antenna steel) and the solar panel installation to make sure you are in compliance - for example they may have limits on lengths of wiring to their ground rod(s).