Since, as I can see, you do not seem to be having any implementation problems, I would focus rather on design aspects than on code and timestamp format. I have an experience of participating in design of network support for a navigation system implemented as a distributed system in a local network. The nature of that system is such that there is a lot of data (often conflicting), coming from different sources, so solving possible conflicts and keeping data integrity is rather tricky. Just some thoughts based on that experience.
Timestamping data, even in a distributed system including many computers, usually is not a problem if you do not need a higher resoluition than one provided by system time functions and higher time synchronization accuracy than one provided by your OS components.
In the simplest case using UTC is quite reasonable, and for most of tasks it's enough. However, it's important to understand the purpose of using time stamps in your system from the very beginning of design. Time values (no matter if it is Unix time or formatted UTC strings) sometimes may be equal. If you have to resolve data conflicts based on timestamps (I mean, to always select a newer (or an older) value among several received from different sources), you need to understand if an incorrectly resolved conflict (that usually means a conflict that may be resolved in more than one way, as timestamps are equal) is a fatal problem for your system design, or not. The probable options are:
If the 99.99% of conflicts are resolved in the same way on all the nodes, you do not care about the remaining 0.01%, and they do not break data integrity. In that case you may safely continue using something like UTC.
If strict resolving of all the conflicts is a must for you, you have to design your own timestamping system. Timestamps may include time (maybe not system time, but some higher resolution timer), sequence number (to allow producing unique timestamps even if time resolution is not enough for that) and node identifier (to allow different nodes of your system to generate completely unique timestamps).
Finally, what you need may be not timestamps based on time. Do you really need to be able to calculate time difference between a pair of timestamps? Isn't it enough just to allow ordering timestamps, not connecting them to real time moments? If you don't need time calculations, just comparisons, timestamps based on sequential counters, not on real time, are a good choice (see Lamport time for more details).
If you need strict conflict resolving, or if you need very high time resolution, you will probably have to write your own timestamp service.
Many ideas and clues may be borrowed from a book by A. Tanenbaum, "Distributed systems: Principles and paradigms". When I faced such problems, it helped me a lot, and there is a separate chapter dedicated to timestamps generation in it.