Is it possible to form a custom private key? For example, could one 'set' the first 2/3rds of the characters - and compute the remaining 1/3 to form a valid private key?
The private key is a number.
Just a number between 1 and 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4140
Any number in this range is valid private key ready to use
https://en.bitcoin.it/wiki/Private_key