I would go ahead and reheat all of the solder joints on that PC board. You are unlikely to damage anything on there from overheating.
If you have 12V coming out of the 6.3V pads, you power transformer connections are unlikely to be a problem, but the 1085 regulator isn't doing its job. This could occur due to soldering issues, an MJE5731A swapped in instead of the 1085, or possibly you have a meter that isn't working properly. To rule out the meter, you can try measuring a 9V battery with it.