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timeGetTime seems to be quite good to query for system time. However, its return value is 32-bit only, so it wraps around every 49 days approx.
It’s not too hard to detect the rollover in calling code, but it adds some complexity, and (worse) requires keeping a state.
Is there some replacement for timeGetTime that would not have this wrap-around problem (probably by returning a 64-bit value), and have roughly the same precision and cost?
Nope, tracking roll-over requires state. It can be as simple as just incrementing your own 64-bit counter on each callback.
It is pretty unusual to want to track time periods to a resolution as low as 1 millisecond for up to 49 days. You’d have to worry that the accuracy is still there after such a long period. The next step is to use the clock, GetTickCount(64), GetSystemTimeAsFileTime have a resolution of 15.625 milliseconds and are kept accurate with a time server.