I don't have a '67 in front of me to look at, but that doesn't sound right (to have to remove the backing plate).

The "inaccessible" bolt by the brake line - are you married to the idea of removing it with a socket, and haven't tried a box-end wrench on it? (Probably unlikely, but I thought I'd ask anyway.) Also, if it's just a matter of having enough clearance to back the bolt ALL the way out, just remove the other bolt first, and let the WC pull away from the backing plate as you turn the remaining bolt, effectively leaving the bolt head where it is.

If none of this applies, then try removing the brake line. You were going to have to separate it from the WC anyway, so all this adds to the project is the need to remove the other end of the rubber line (so you can spin it out of the WC).