EAP-MD5 authentication for WAN interface

I recently upgraded our broadband and my internet broadband operator supplies a modem + a "home gateway" (HGW) router that you are supposed to use for connecting to their internet. The modem and HGW connect with RJ45, and I would much rather use my OpenWRT based router to talk to the modem as I used with the previous broadband setup.
In the past it was enough to just use same MAC address what the modem expected and you could continue on your merry way, but with this new gateway, it does not seem to work so.
I did some snooping around with wireshark, and it looks like before the modem initiates a EAP-MD5 handshake before DHCP exchange takes place.

I can see the successful exchange with HGW:

36	54.179225744	ThomsonTelec_63:ff:01	AskeyCompute_9a:92:21	EAP	60	Request, Identity
37	54.179851963	AskeyCompute_9a:92:21	Nearest-non-TPMR-bridge	EAP	60	Response, Identity
38	54.185401327	ThomsonTelec_63:ff:01	AskeyCompute_9a:92:21	EAP	60	Request, MD5-Challenge EAP (EAP-MD5-CHALLENGE)
39	54.186934636	AskeyCompute_9a:92:21	Nearest-non-TPMR-bridge	EAP	60	Response, MD5-Challenge EAP (EAP-MD5-CHALLENGE)
40	54.193137788	ThomsonTelec_63:ff:01	AskeyCompute_9a:92:21	EAP	60	Success

Now, with OpenWRT, since by default there is nobody responding to EAP requests the modem keeps sending Request, Identity messages forever and nothing happens.
The HGW identifies itself as "H15HG1574979":

Frame 37.... 
<<snip>>
Extensible Authentication Protocol
    Code: Response (2)
    Id: 1
    Length: 17
    Type: Identity (1)
    Identity: H15HG1574979

So I did some research into the matter and it seems like wpa_supplicant could help here, and I configured it as such:

$ cat /etc/config/wpa_eap.conf
ctrl_interface=/var/run/wpa_supplicant
ap_scan=0

network={
    key_mgmt=IEEE8021X
    eap=MD5
    identity="H15HG1574979"
    password=""
    eapol_flags=0
}

Now if I start the supplicant with wpa_supplicant -Dwired -i eth0.2 -c /etc/config/wpa_eap.conf -d I can actually see the OpenWRT router responding to the EAP request, but modem complains about a failure.
This is pretty much where my understanding about EAP works comes to an end, and all I can do is compare two wireshark traces. When comparing the two wireshark traces, I can see following difference in the EAP challenge response:

OK:
0000   01 80 c2 00 00 03 08 33 ed 9a 92 21 88 8e 01 00   .......3...!....
0010   00 22 02 02 00 22 04 10 42 ed bb 51 56 27 33 9a   ."..."..B..QV'3.
0020   92 03 d3 44 8b 0e 17 b8 48 31 35 48 47 31 35 37   ...D....H15HG157
0030   34 39 37 39 00 00 00 00 00 00 00 00               4979........

NOT OK:
0000   01 80 c2 00 00 03 08 33 ed 9a 92 21 88 8e 01 00   .......3...!....
0010   00 16 02 05 00 16 04 10 7a 27 ec aa 17 57 3c c2   ........z'...W<.
0020   4d 07 6c a2 36 e3 cc eb 00 00 00 00 00 00 00 00   M.l.6...........
0030   00 00 00 00 00 00 00 00 00 00 00 00               ............

Essentially it appears that when sending back the challenge response, the HGW sends again the identity bytes as EAP-MD5 Extra Data: (the last bytes from above "OK" case, 48,47...)

Frame 39...
<< snip >>
Extensible Authentication Protocol
<< snip >>
    EAP-MD5 Value-Size: 16
    EAP-MD5 Value: 42edbb515627339a9203d3448b0e17b8
    EAP-MD5 Extra Data: 483135484731353734393739

How would I configure wpa_supplicant also to respond in similar fashion? I already tried adding the identity string (H15HG1574979) as password but that had no effect..