I'd avoid adding vinyl. For one you'd want to stick all of them at the same time to avoid the brush strokes going slightly different angles, but most metallic vinyls have aggressive adhesive, so it may rip up bits of wood surrounding the sign if it accidentally touches the background. Then you'd obviously need to hand trim all the letter, on the wall, presumably during business hours. The metal face is crazy thin, so angling your knife too much will divit the edges, and sticking a bit too much knife out will score the background. Not saying it can't be done, I just foresee some major issues if you just lop 6x6 oversized pieces and start sticking them.
At best I'd opt for using some 040 brushed aluminum, apply 3m467mp, route with the adhesive down, then apply the metal to the faces on site. This would put the cost close to or more than a new set of letters though if you don't have the two materials on hand already. Last time I got aluminum brushed it was a minimum order of 5 sheets, and that was 1/8" aluminum, and I believe they priced that by weight. 467mp I've only ever bought in a 60yd roll, even at 12" wide it was something like $300.