I decided on blue masking tape. Actually in the beginning I just decided to use tape again since the black electrical tape worked well at the old place, and comes up easy not leaving a mark on the floor. Any residue cleanable with something like 409. So when I wandered into the basement to find it I saw this stuff sitting on top a shelf, left over from painting. I thought, Hey. It's medium stickiness so should come up pretty easy, it is wider than the electrical tape, and is nicer looking.
Putting the oche down also gave me the chance to double check my math. The 7' 9.25" is supposed to be from the face of the dartboard, not from the wall, so adding this distance to the thickness of the board and backboard combo I get 7' 11.75". But then subtracting the thickness of the baseboard and cord a round I really end up with 7' 10.5", which as I'd measured before, really DOES correspond exactly to a line in the hardwood floor. Nice to have an official oche anyway.