Dear Vladimir,
1) Yes, I see it reasonable to not use local times but a common time scale all over the universe. Lorentz introduced local time as to rescue the ether hypothesis. Einstein applied Poincaré synchronization against logic to moving relative to each other AB too.
2) Yes, distortion of space and time is not necessary.
3) I do not see an ether lattice required. In that Einstein in 1905 was perhaps correct, by chance.
4) I am not sure if I understood what you meant.
Regards,
Eckard