There is a lot of misunderstanding regarding BC's that is true, the most common one being that BC varies with speed. BC will have small changes with speed, since any reference drag curve cannot match the drag curve for every design of projectile. However, the fact is that in the vast majority of cases, large changes in BC with speed are entirely due to the use of an inappropriate reference drag law. When the correct reference drag law is used, a single value of BC will be correct at all speeds, this is the entire basis of the BC system as it was originally envisaged. Many of the so-called experts who claim BC always varies with speed basically do not know what they are talking about., as they are using the wrong reference drag law.
The biggest example of the wrong drag law and the one which clearly shows up the problems is the use of G1 for large meplat slugs as represented by the majority of available slug designs. Below is a calculated drag law for a 5% meplat .22 30grain slug compared to the G1 reference drag law. Yes the slug drag law is calculated but data being collected suggests it is a good initial representation of slug drag, showing substantially smaller changes in BC with speed.
View attachment 369222 The reference drag law is supposed to be the same shape as the actual drag law, and clearly it is not, leading to multiple BC values being needed to try to approximate to the real shape. This means that G1 based BC values at around 1000 ft/sec are hugely optimistic for any other speeds, but it enables manufacturers to make claims for measured BC values.
There is another point which many do not seem to grasp. The increased BC value at high speeds does not mean the drag is miraculously reducing at higher speed. You can see from the actual drag curve it is still increasing, just not as much as the G1 drag law and hence the increased BC value.
In terms of down wind drift, BC is also somewhat misleading. If a perfect reference drag law is used and a single value of BC can be used, that does not mean the drag coefficient is not increasing. You cannot see the drag increase in terms of the BC value because it is hidden in the reference drag law. So your drag coefficient is increasing with speed and giving increased cross wind effect and more down wind drift.
Neither is down wind drift a function of time of flight. It is a function of the "lag time" (not usually called lost time) which is the difference between the actual time of flight to the target and the time of flight if there was zero drag. This means that if your actual time of flight is the same as the time of flight with no drag there is zero down wind drift. This has been shown on many occasions with projectiles with a form of propulsion. It has also been shown that accelerating projectiles which have a negative lag time drift up wind, not down.
On the question of speed and the effect of muzzle velocity on wind drift, as said, Bob Sterne has shown diagrams on many occasions demonstrating the effects of increased speed on wind drift. I knocked out the diagram below for the slug described above using the actual drag law, not BC or G1. The model is similar to ones I used when working which use purpose drag laws, not BC.
View attachment 369228 In every case at all ranges the minimum down wind drift is around just below 1000 ft/sec. The longer the range, the more the drift increases at higher speeds. The reason they are all have the same optimum speeds no matter what the range is probably because the optimum speed is a function of the drag curve shape rather than the range which you may expect.