I have an SGS2 but had a similar issue. With ICS 4.0 the MTP seems to show camera only. Amarok and Dolphin recognise the MTP device but can't do anything with it.
I ended up using AirDroid to provide a web interface over local WiFi. Prior to this I had OpenSSH server running on my laptop and used AndFTP on my phone to move files back and forth.
If all else fails you could always try one of these methods.
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