First off, I don't think it would work, at least not well enough to justify spending $200 on the tax, and whatever else you'd need to spend for the outer shell. You might get a very minor reduction in the sound signature - maybe a couple decibels, but not enough to justify the cost. Any reduction in sound signature, however, will make it a suppressor in the eyes of BATFE so even though it might not sound like its doing much, it would still need to be registered. If you're going to get a suppressor and you don't have the ability to make a proper suppressor yourself, you should buy the best you can afford from a reputable manufacturer since you'll probably be stuck with it. Even high end suppressors are hard to sell once on a form 4 due to the cost of the tax in comparison to the cost of a new can.
Second, you need to get an approved form 1 before you start making any NFA item. You don't get the "permit" after you make it, you do the paperwork first.