Wrong jetting will cause to run lean/rich, but not to cut out. Plugged jet would cause it to run poorly, or not at all, including when its cold. So I think for now I would look elsewhere. I am a carb man, have worked on lots of carbs, and it just doesn't show any symptoms of a bad carb. However, taking off the float bowl and verifying what jets you have might be a good idea. That has little to do with your problem though.
Stay strong, you also might want to get some advice on BuellRidersOnline.com as there are quite a few very knowledgable blast guys on the site that are very quick to troubleshoot. There are also blast owners that have experience with that module on the site.