340 build
Waste of time to work over the pistons for piston to head clearance. My son's 340 has the pistons above the deck with the same heads, and we just adjusted the gasket thickness like you have been encouraged to do.
You DON'T have the wrong heads at all. (In some ways, what you have is a better chamber. ) You just adjust the head gaskets to work with what you have. The heads with the recesses machined on the underside of the heads just come that way so you don't have to work over the piston with standard head gaskets. Both head flow and work the same.
A local machinist who does tones of 4 banger races engine uses .025" as a minimum; he has seen the the pistons kiss the heads with that clearance. That is for racing. AJ may have run .023" but that is VERY marginal. The general rule of thumb for .035" clearance allows for a lot of variations. It also allows for more bore wear over the long term; as the bores wear, the pistons will rock more and more and the high point of the piston gets closer to the heads. If AJ was using hypereutectic pitons the are a lot tighter in the bores and don't rock nearly as much as the forged pistons that you have; so those pistons can be run at a tighter head to piston clearance. Your pistons are going to be on loose side with more rocking so beware. Long term for TROUBLE-FREE operation, work with the .035" piston to head minimum clearance.
Now if you really want to spend the $$ on the piston machining to use lower cost head gaskets, and it costs you nothing, then go for it. But I would not go .010" below deck. I would stay .005" above deck with the tallest piston and use a .039 thick Felpro 1008 head gasket. You then have .035" head clearance to the tallest piston, and .044" to the shortest. (And you may be able swap rods around to get less height variation.)
The reason to keep the gap in the .040" range +/- is for something called quench; read up on that term. It helps reduce any tendency for the combustion process to detonate, which can be a piston destroyer. With the AL heads, small combustion chamber and the tight quench gap, you are as good as you can get in that regard. It will be good to do all you can in this area of eliminating detonation for running this engine in a heavy truck.
Valve to piston clearance is another matter entirely.