I should explain: There are two trees of heaven.
One is an ornamental species that is often planted where quick growth is needed, and the other is an ornamental species that is planted in north america.
I live in europe. The species Ailanthus altissima is the european one and is diffuse porous. The bark fits as does the purplish coloration and density. It is likely that this species is often found in north america but not known as tree of heaven because it's a "usurper" species.
That said, he is in north america and not in europe so...
My guess, though possible, is unlikely.