I went over your file and test printed both your file and a revised version I made with corrections to issues detailed below. Your basic setup was correct but one or more of the issues below may be causing your problem. I am emailing you back the revised file for you to test.
The test prints of both your file and my revised file ran satisfactorily. There was a slightly rougher appearance with your file due to the higher heat settings you were using.
Vinyl Assignment
Your vinyl assignment was for Gerber 220 White although your intent is to print it on an unspecified clear vinyl. It won't matter all of the time, but it is good practice to assign the closest vinyl to what you will be using for the job as it may effect the firing settings for each foil. I reassigned your vinyl to Imagecast Clear.
Close Tolerances
The nature of your artwork and the size you are printing at may be part of the problem. The outline is unusual in that the inner line is radically different from the outer line. It has lots of thick and think spots. In the thick spots, you are working with about .015" sizes. In the thin spots, there are even some overlapping vectors which Omega may not handle as one might expect. Recall that I mentioned earlier the tolerance of an Edge is about + or - .020". The point is that this job at this size is problematic. I have corrected the overlapping vectors and also done some selective adjusting of the widths between vectors in the overlapping areas.
Overprint Versus Overlap
The black and the red were both set to overprint. This setting, as opposed to overlap, turns up the heat of the printhead. The result is a harder, rougher result. This may be one of the primary contributors to the results you are getting. I have set the vectors to overlap rather than overprint.
When in Doubt - Slow Down
Since you are using an Edge II and I had no problems running it on my Edge LE, I must ask what speed and resolution settings you are running the job at? In a tight tolerance job, slowing down to Edge I speeds and using the 300 x 300 DPI settings will likely improve your results since there are nothing but solid colors in the job anyway.
As I said though, your unmodified file ran fine for me except for some minor roughness which I attribute to your overprint settings. So I think the likely reasons for your difficulty are that it is a tight tolerance job and you are running at too hot a temperature setting because you are using overprint rather than overlap. In addition, if you are running at higher than Edge I speeds and resolution, this would exaggerate the problem.
I am sending you the revised file by email. Let us know how things work out with my various suggestions.