Forced lines all along

Last post, I covered a line in the Teichmann defense 1.d4 d5 2.e4 dxe4 3.Nc4 Nf6 4.f3 exf3 5.Nxf3 Bg4 6.h3 Bh5 7.g4 Bg6 8.Ne5 e6 9.Bg2 c6 10.h4 Bb4 11.Bg5 ?!

I showed that white is on top aftre the natural move 11...Nbd7 12.h5.

Unfortunately for the line, black has some otehr choices. as an example, Scheerer indicates 11.Bg5 to be "dubious" and suggests 11...Qa5 after which 12.Bd2 Qb6 13.h5 Qxd4 14.Nf3 Qxg4 15.hxg6 Qxg6 "...Black has four pawns for the piece and went on to win in E.Stadler-G.Haika, correspondence 2000."

Hmm, that's a bit of a setback. Let's start at 11...Qa5 12.Bd2 (diagram)

My silicon assistant only gives 12...Qb6 here ( 12...Qc7 13.Qe2 += ) followed by 13.h5 Qxd4 14.Nf3 (diagram)

Again, Scheerer's line is confirmed and 14...Qxg4 15.hxg6 is suggested.
Black may deviate now with 15...Qxg2 but this greedy capture is punished by 16.gxf7+ (+)
Another option is 15...Qg3+ 16.Kf1 but this is better for white than the main line.

So Scheerer was completely right - black has 4 pawns for the piece. But is black also winning ? Let's look after 16.Qe2 (diagram)

Faithfull Houdini now suggests 3 lines

a/ 16...Bxc3 17.Bxc3 Qg3+ 18.Kf1 (+=)

b/ 16...Qg3+ 17.Kf1
...b1/ 17...Nbd7 18.Rh3
......b1a/ 18...Qc7 19.Nb5 cxb5 20.Bxb4 Nd5 21.Be1 (+=)
......b1b/ 18...Qb8 19.Ne1 (+=)
......b1c/ 18...Qd6 19.a3 (+=)
......b1d/ 18...Qg6 19.Nb5 (+=)

...b2/ 17...Qc7 18.a3 (+=)
...b3/ 17...Be7 18.Rh3 (+=)
...b4/ 17...Bxc3 18.Bxc3 (+=)
...b5/ 17...Qg6 18.Nb5 (+=)

...b6/ 17...00 18.Ne4 Nxe4 19.Qxe4 (++)

c/ 16...Qxc2 17.Nd4 Qxb2 18.Rb1 Qxc3 19.Rxb4 !!

...c1/ 19...Qc5 20.Rh4 (=)

...c2/ 19...Qg3+ 20.Kf1 00 21.Rxb7 (+=)

...c3/ 19...Qa1+ 20.Kf2 Qxa2 21.Nf5 (++)

So it seems to me that Scheerer was right - white has to give an awfull lot of pawns for the piece. But I disagree that black is winning. Its seems to me only line c1 gives black an equal games, and white is on top in all other lines, even if white has given 4 or 5 pawns for the piece.