Testing with the ohmmeter and the light bulb in the beginning, with the rectifier tube out, is the way to test the power transformer for shorts. If there's a short in that, you're in for a relatively big expense and you may decide that the set either is or is not worth fixing at that time. It's easy to do that now at no cost rather than recap and find out the bad news later. At least you know where you stand going in. When the bulb lights "dim" you let out a big "phew!"
Reece