A quick Google turned up an app called SSHDroid. Looks promising. I've not tried it personally. All I do is use my phone as the client (AndFTP) and the desktop machine (Running openssh-server) as the server.
I know you pretty much dismissed wireless (i.e. over the network.) solutions but for me, losing a little speed is worth the convenience of not having to get off the sofa to physically plug into whichever PC I want to transfer to. I guess I'm just too used to transferring over the network using sftp as opposed to sneakernet.