lights on when they are not, specially when appear very bright at times, is typically a lamp column problem. Usually it is a blown main driver transistor but occasionally deeper into logic problems.

Still sounds like lamp column problem. Burnt to a crisp 27ohm resistor is a symptom of locked on lamp column problem, not normally the cause of the problem. The columns are strobed, when it locks always on there is constant load on the 27R 3W resistor that does current limiting on the base of the main transistor and it burns up.

If you replace only the resistor pay close attention to see if it rapidly heats up more than the others. Very likely there is something else still wrong from the PIA, 7408, or transistors. Normally it is just the main driver transistor but with a logic probe you can start at the PIA and trace towards the transistors and see where it locks on at. If you are unsure what to expect on the logic probe compare to working circuits.

Lamp row issue usually end up being all the lights off. Lamp column issues is extra lights on.... in typical fail modes at least.