Probably the most accurate time base you can provide remote Arduinos is using the pulse per second (PPS) option on GPS receivers assuming you have receivers at each Arduino, it is used to re-zero the clock, but the Arduino crystal is still the timer. Trying to provide resolution of 10-9 sec with a clock that has a crystal with a period of 6.25 x 10-8 sec. is not going to work.
How is the device going to ingest the data from the four Arduinos at the same time without some buffering? Do you have 4 receivers or does the receiver have a baud rate fast enough to collect 4 messages inside of a couple nanoseconds.
I think you need to explain in detail what you are trying to do and then the incredible body of experience here may be able to help, all we can do without detail is tell you why it won't work not how you achieve your desired result.