When the disc is all the way down it is in the play postion. I am fairly certain it won't pull out easy that way. Like I stated earlier, I just try to spin the disk and then install the cartridge wait a few seconds and hit the eject button to kick it back out if the player sees the disc in the play position it will eject it into the cartridge prior to ejecting. I do this with the car off and the radio off.
I guess if the disk is truely stuck, it is not too bad to remove the unit and take it aprt. I have done that as well to oil the mechanism and such. The power wire comes from the power ant. and the radio cable unplugs from the unit. 30-45 minutes of work to remove. Take off cover, remove the stuck disc, and 30-45 minutes to put back in.