Out of interest, the Lioy study found Al levels of ~800,000 ng/gm or 0.08% by weight in the dust samples. For reference, a selection of metals in the dust (though not necessarily elemental) included:
Aluminium ~ 800,000 ng/gm
Strontium ~600,000 ng/gm
Titanium ~ 1,600,000 ng/gm
Manganese ~ 700,000 ng/gm
Lead ~ 300,000 ng/gm
In other words, if there was in fact any unspent aluminothermic material in the dust its action on subsequent ignition in the debris pile would be utterly swamped by the sheer mass of other material. My sake-of-argument allowance of 5% by weight, earlier in the discussion, was meant to be over-generous. In fact it was insanely high, especially given that much of the Al detected would be from naturally occuring compounds.
Although Lioy et al. didn't go looking for thermite, their figures comfortably allow us to rule it out as a source for molten steel in the debris.