I’d go for a small server that returns a unix timestamp, the client fetches it, computes the clock drift (difference in time) and all the protocol related times are based on that drift. The clocks would still drift a little (they’d do it anyway on the system clock) and we would not get perfect synchronization (impossible in distributed systems), but it would solve our current problems.
The code is about 5 lines and some simple math (sums) when calculating the timestamps.