The ULN2003A has a typical output voltage loss of 1V and it could be more.
With the resistors in series with the relay coil then it will have a typical coil voltage of only 2.9V or less in one direction and only 3.8V or less in the other direction and probably won't work.
Paralleling the outputs does not help since the coil current is low.
With the resistors in series with the relay coil then it will have a typical coil voltage of only 2.9V or less in one direction and only 3.8V or less in the other direction and probably won't work.
Paralleling the outputs does not help since the coil current is low.