ESD tape is conductive and can act as a shield for RF devices (the BT module).
- personally, i wouldn't use it. i see too many possible issues that could arise from using it.
- it's conductive, wouldn't want to use it on any exposed pad or solder point
- because of the "traces"/grid in the tape, it can act as a shield, and could make your wireless signal worse depending on where/how the tape is applied.
- if the board is manufactured correctly, there shouldn't be a worry of a fire hazard. just don't poke or puncture the battery when modding. if it's taped down, leave it taped down. if it's just a little LiPo bag battery, you could damage it trying to peel it off the bottom of the case (IF that's how it's mounted. i'm not familiar with this board other than the images in the link)
- i just see the ESD tape causing more issues than solving problems.
- looks like the plate is FR4 (same material as pcb) is that correct? (at least it's not an aluminum integrated/top mount, can be very noisy)
- you'd probably effect the sound the most by lubing or changing switches. (adding another matte/foam/other material to the case might not effect the sound much)
- what switches are you using?
- are they lubed?
- what don't you like about the sound? what are you trying to change?