There was a huge contraversy over the Fat Finger when it was released. Some swore that it helped fatten the tone, while others removed them, vowing NEVER to add more weight to the headstock again. I installed a set of Sperzel locking tuners to a PRS Custom a while back in hopes of remedying some tuning gremlins. The guitar's tone was DRASTICALLY changed.........so much that it caught me off guard. The guitar lost its low-end, and seemed to gain some odd 'crispness', or brassiness. I hadn't expected the heavier Sperzels to 'sound' any different than the lighter Shaller-made factory PRS tuners. That was enough for me. I put the factory tuners back on.
I've never tried the Fat Finger myself, and doubt that I ever will. Maybe the design of the device CAN help the tone of a particular anemic Strat. It is brass, correct? That may have a different effect than a set of heavier diecast metal tuners. The flat plate-like Fat Finger could, in theory, resonate with the headstock, while I doubt that the tuners are even capable.
Think about the effect that deadener rings have on drum heads (They're typically used to tame drum heads in the studio). They're thin donut-shaped perimeter rings that are merely laid on the head itself, and not very heavy at all, but they'll kill a 'ringy' drum like nobody's business.
Sure something to think about......
Mike