The A70 is right up there though, and if you are replacing a Type A, it probably fits into the hole. The Lab 80 cutout and the Type A cutout are very different. The A70 has a counterbalanced arm, the same trip linkage as the Lab 80, same headshell as the 80, and I believe its the same motor as well, but it may be the similar 4 pole motor from the Type A. The 80's motor is probably better isolated though. One other plus to the A70 is that the side pusher mechanism is 78-friendly, and of course the machine will run 78 rpm.
An A-II is essentially identical to a Type A, other than the paint job. There would be no good reason to swap one for the other unless there are fatal flaws. besides, the original cream color Type A is a better looking rig IMO. The A70 is also largely similar, though with a better arm and better trip system.