Will these heads work?

I have two sets of J heads casting numbers 3418915 on both, one set has 2.02 intake valves the other set has 1.88 intake valves. I have a 340 Casting number 2780930-340-4, I'm going to build. I read someplace but can't find the site again. The #3418915 AAWJ 360 2.02 is a T/A head. But,they claim they will not work on a LA engine block.They said,they would bolt up, but will not work. Has any one else heard of this? What head should I use?