My all time favorite way to cook Abacore is to mix up a marinade of good olive oil and splash of red wine vinegar a whole bunch of fresh Itilian parsley chopped coarsely, 4 to 6 cloves of garlic chopped fine and the juice of 2 lemons, sea salt and a heathly bit of cracked black pepper. You can marinade whole loins over night or 1 1/4" medallions for 3 to 5 hours, then grill hot and fast until the tuna is done all the way through. This marinade is awesome on cracked crab even pork loins and chops.
I ate so much albacore growing up that you would think I would be sick of it.
Nope the only thing I hate about Abacore is the smell of the tuna boats my family owned in southern California. My mom's side of the family pretty much all worked in the tuna industry. Both fishmen and working in the Delmonte packing plants on the landings.
Sorry about the crappy post, Im pecking away on my phone in the dark. LOL