You can order the mechanism (and any other parts) either directly from JVC or from Andrews electronics. But, I guarantee you're not going to like the price of the mechanism - about $136 if you get the LG part (for BD370), or $368 if you get the JVC branded part. Obviously it doesn't make a lot of sense to fix this unit rather than purchase a new player.
I know I'm rather late to the party, but I just purchased a never used XV-BP1 player for $100 and I'm loving it already. It's definitely made a noticeable improvement to DVD playback on my new Sony LCD.