Are Xilinx XC7A35T actually the same die as something else or...?

[mrflibble]

Is it possible that LX4 uses LX9 die but with whole sections being unpowered?

In the land of the theoretical anything is possible. However not equally likely.

Given the triples (bitstream size , quiescent current, IDCODE) it does not seem likely. Furthermore it would be the only die in the entire spartan-6 family where they did a die reuse. Compared to how the 7-series is segmented, it just does not seem likely. So I am going with a big fat nope.