Let me know what progress you make if you have it apart, still not got mine so I can only plan stuff going on photo's of its internals.
No toy shifter is gonna feel like the real deal though, espically a compact one like the Logi one, where there isn't space to simulate a realistic feel of a gearselector. Fitting a stiffer spring should be easy to do though, assuming you don't mind it being stiffer in sequential mode as well.
About the push-down reverse..unless the spring for that is weak enough that resting your hand on the shifter will cause it to start compressing, it isn't unrealistic. My old Ford Escort had a pushdown reverse, never caused a problem.