I think I'm ready to say what the problem is.
To review - I've made sure the old Mini and both new Minis have the same fuses, bootloader and test sketch. All the boards look identical. With the regulator and power LED removed, there isn't much left on the board that could account for the high sleep current in the new Minis.
This morning I tested the theory that the big cap on Vcc was leaking, With the regulator removed, the big cap on the Raw input wasn't used anymore. So I connected its plus end to the Vcc cap (same size = 10uF), and tested the Mini again. My thought was that if adding the second cap to the output did not change the sleep current, then at least I know the Raw cap isn't leaking.
And sure enough, the sleep current was still 150uA.
So with a known good capacitor, I removed the Vcc cap, leaving only known good one in the circuit. If the Vcc cap had been leaking, the sleep current would now drop to 1uA.
But the sleep current stayed at 150uA.
So I think I'm ready to declare that the board and its parts are ok, and the problem is the processor. I don't know specifically what's wrong. It could just be a bad run, or a mis-labeled part, or a counterfeit, but the processor seems to be the problem. I think confirming evidence is the big difference in current drawn between old and new when I ground the reset pin. There's nothing on the board except maybe the resonator that could have any effect on reset current.
I don't have any rework gear that would let me switch the processors, and the odds that I could do that successfully with my soldering iron are very low. So unless someone has another idea, I think I need to give up on these. Whatever is wrong is nothing I can fix.
I guess I could do some destructive testing - removing everything else from the board except the processor and resonator, and might even reflash it to use the internal 8Mhz oscillator, then remove the resonator. But my guess is the sleep current is still going to be 150uA. I thought it might be possible that the new ones are 328, not 328P, but that's not right. Both the old and new ones have a 20uA increase in sleep current if the BOD is not disabled. There would be no increase with a 328.
So I'm going to order another batch from another source if I can find some with different markings on the 328P. I just wish I was able to pin down what's actually going on with the processor.
Thanks to everyone for the comments and suggestions.