That was a good test, What we learned is that:
1) As we thought your machine is working well.
2) The possible problems are really narrowed down now to the two I told you about in the earlier post.
Possible Problem 1:
The 1/8 detail bit is not being zeroed correctly. I know you are certain you zeroed correctly so for now lets remove this as a potential source of the problem.
Possible Problem 2:
The bit is slipping in the collet
Based on the videos you show and the tests you have done, these are really the only two possible causes of the error you are seeing.
If we eliminate problem 1 then that only leaves problem 2. So the 1/8 inch bit is slipping when you cut.
Since you purchased a good 1/8 inch collet I don't think the problem is with the collet (we can test that later). So that only leaves the 1/8 inch bit itself as the source of the problem.
The only way the bit can cause the problem is if the shank diameter is less that .125 inches. If you have a micrometer measure the diameter of the shank of that bit and see what the actual diameter really is. Maybe you somehow got a bit with a 3mm shank.
So that is where we are at, either the bit is the problem or the collet you purchased is defective or you are not zeroing the 1/8 inch bit correctly.
We can test the collet by using a different 1/8 inch bit and see if you still have the problem, If all your 1/8 bits are slipping then it must be the collet. If the other bits do not slip then we are back to the first bit being an odd size or the zero is not set.