The only way you could remove the BIOS chip from the socket is if you have a pre-production NUC, and I'm sorry to say that we cannot replace pre-production units. All production units have the chips soldered down. The only other option I can suggest is to remove the jumper, and force the BIOS recovery: BIOS Recovery Update Instructions for Intel® NUC and as a last resort, remove the battery to clear the CMOS.
In fairness I have asked for a BIOS file dump - not a replacement for it; I did mention that recovery was performed and failed after which the recovery itself was "bricked". It is a last resort to revive it before getting securely disposed for reason you mentioned. But it would be a shame.
Feel free check account/PM me/etc if you have any concerns about the "legality" of the NUC ownership.
That is not something we have access to. Only what you see already on downloadcenter, or if there's a removable BIOS chip. I trust your ownership, it's just not something we have. The only reason I mentioned the jumper is that there are 2 ways to do recovery, and I just wanted to make sure you knew that. One with the power button, one with the jumper. The NUCs do have a 3 year warranty, so if it's within that time, please create an RMA: https://customercare.intel.com/