It just so happens that I was on one-week's vacation when Dennis Monokroussos posted his first in a series of blog entries on the Philidor Counter Gambit, which explains how I was able to respond as quickly as I did.
But now the burden of working full-time at the law firm, tutoring a chess student in the evenings, playing in tournaments on weekends, and maintaining a daily blog has taken its toll, leaving precious little time for me to analyze deeply the many lines that Monokroussos has suggested. But I am studying his recommendations, one by one!
For instance, in the variation 1.e4 e5 2.Nf3 d6 3.d4 f5 4.Nc3 fxe4 5.Nxe4 d5 6.Neg5 exd4 7.Bb5+ c6 8.Bd3 Bb4+ 9.Bd2 Bxd2+ 10.Qxd2 Nf6 11.O-O-O O-O 12.Nxd4 Re8 13.Rhe1 h6 14.Rxe8+ Qxe8 15.Re1 Qh5, I must admit that Monokroussos's 16.Ngf3 is an improvement on my 16.Nge6.
On 16...c5 17.Ne2, Black's queen will soon be embarrassed after 18.Nf4.
Since Black's idea is to encourage 16.Nge6, the move 15...Qf8 (instead of 15...Qh5) comes to mind.
A likely continuation is 16.Nge6 Bxe6 17.Nxe6 Qd6 18.g4 Nbd7 19.g5 Re8 20.Bf5 hxg5 21.Qxg5 Re7 22.Rg1 Ne8 23.Nd4 Qf6 24.Qg4 Nf8 with an equal position.
It also occurs to me that, in the line 7.Nxd4 Qe7+ 8.Be2 h6 9.Ngf3 c6 10.O-O Qf6 11.Re1, the move order 11...Bb4 12.c3 Bd6 may be a refinement on the immediate 11...Bd6.
At least, after 13.Ba6+ Kf7 14.Bd3 Ne7, White no longer has the maneuver 15.Bd2 followed by 16.Bc3 at his disposal.