I would recommend that you skip the vinyl routine for a few reasons.

1. It's a pain to work with, and you will find it very difficult to get it to lay properly if you ingrave the JL logo. I also wouldn't go cutting up your box either.

2. It's going to show all of the imperfections of your box. Namely, the caulking on the outside of the box. I also noticed you have an uneven edge there....you'd have to do a lot of sanding.

I'd suggest you take some 1/2" or even 1/4" MDF and cut the jl logo out of that. Attach it to your box, then carpet over the whole thing. Carpet is much more forgiving, and it will show the logo through. Not a criticism, just a few suggestions!