I am right in believing that all of Einstein's theories were based on thought experiments rather than the results of direct observations. If this is the case is there any reason why he could not have arrived at his theories at any time after Newton?

no he could not as the thought experiments are based on some theories(such as the maxwell equations). seeing as those were not around(ond some of the observations such as the precession of mercury) the theories would not have been postulated.

Many people think that (special) relativity would have been discovered about that time whether Einstein was there or not. There is a view that in the case of most new science, the cards were right for the new advances, and they would have occurred about that time whether there was a great scientist around or not. The great scientists would mostly speed things up. In some cases, though, there were significant discoveries that were not based on earlier science -- eg Newtonian mechanics.

The math he needed didn't exist 100 years earlier. Einstein tensors, on which Einstein's Field Equations are based, were born from the tensor calculus developed by Gregorio Ricci around 1890...

Maxwell's equations didn't exist, and Michelson and Morely's experiment hadn't been done, so there really was nothing to prompt his relativity theories.