Earlier Sources, Once More

Returning to Peter J. Monte's The Classical Era of Modern Chess (2014), searching for precursors of the Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) we have already seen that in the 1590s Giulio Cesare Polerio explored 1.e4 e5 2.Bc4 Bc5 3.Bxf7+

He also looked at White placing his Queen on e2, to be able to follow up on 4.Bxf7+ with a Queen check fork. For example 

1.e4 e5 2.Bc4 Bc5 3.Qe2 c6 4.Bxf7+ Kxf7 5.Qc4+;

1.e4 e5 2.Bc4 Bc5 3.Qe2 Nf6 4.Bxf7+ Kxf7 5.Qc4+ d5 6.Qxc5 Nxe4 7.Qe3 Re8 8.Nf3 Nc6; 

and 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Qe2 Nf6 5.Bxf7+ Kxf7 Qc4+ d5 7.Qxc5 Nxe4

It is disappointing to see that the main Jerome Gambit line - 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ - doesn't show up in these very early sources. In part it seems that the Queen check at c4 (after Qe2) was where the analysts focused; I could only find one relevant Bishop's Opening line with Qh5+, and the move was labeled as wrong, with no further attention.