and we now have checklists for it...pulling avionics fuses, using an extinguisher, diving to choke-out the fire,
Actually they're memory items. And if it's an engine fire a fire extinguisher in the cockpit will not do you much good. Nor will any of the other items you mentioned. Except, maybe, diving to choke-out the fire. But I wouldn't know how effective that is, considering the relatively low Vne of a typical GA aircraft compared to, say, a WWII Spitfire or Mustang. Anybody knows how fast an Avgas/Air mixture flame front spreads?
Here's what you should do without hesitation:
Close throttle
Close mixture
Close fuel cutoff
Oh, and there's a neat invention called a firewall. It's designed to stop an engine fire from spreading into the cockpit. Works fine as long as you remember to seal it properly - some aircraft may have vent holes or other holes through them, which may require separate actions to close. Cabin heat for instance should be selected "off".