I was curious reading your post so I did a search for your CD player and got some images. Assuming I was looking at the same player you have, the transport looks very easy to replace. Maybe you can buy the transport and install it yourself.
One other thing you can try is moving the remote far away from the CD player. Sometimes, the remote can break in such a way as to send commands without you pushing any buttons. If the player is getting a false input for something like a seek, you can definitely mistake that for a skip. I thought the transport in my Wadia was going bad when the tray kept opening and closing by itself. It turned out to be the remote.
One other thing you can try is moving the remote far away from the CD player. Sometimes, the remote can break in such a way as to send commands without you pushing any buttons. If the player is getting a false input for something like a seek, you can definitely mistake that for a skip. I thought the transport in my Wadia was going bad when the tray kept opening and closing by itself. It turned out to be the remote.