You're applying a principle too broadly. Although the laws of physics don't change under a linear expansion of time, they are, for example, sensitive to linear expansion of velocities of missiles only: any non time-linear effect on the velocity is going to impact you -- for example, reynolds numbers for air depend non-linearly on the velocity which may be varying with time. Sure, if you multiply the whole system you would have that compensated by the increase in temperature and pressure which a faster time reference would observe, but it's not simulating the universe, just a limited set of variables.
Also, for obvious reasons of consistency and precision it would be better to keep a standard reference regardless.
I do not think of the problem as scaling the time by a factor - although this is the correct description - but as adding a constant offset. I think this is justified because the small drift is not significant during the relative brief period of time a target approaches. The offset builds up over time but only in the parts of the system that did not receive the improved algorithm and therefore these different parts disagree more and more on what the current time is.
Also, for obvious reasons of consistency and precision it would be better to keep a standard reference regardless.