Hi Callus,
You're probably going to get asked this question first, so I'll just jump in!
Do you have a teacher? Some bass playing problems are not well solved via internet. . . Okay, now that I've said that!
The way I learned to play is to never rely on the Left hand thumb to hold up the bass, ever. Your idea of having the neck cradled in your shoulder is a common solution that a lot of bass players employ -not me though! I was taught to leave the bass vertical as much as possible, and in thumb position the bass actually leans a bit forward into my fingers.
Here is a video of Gary Karr playing exceptionally well, as always.
It might give you some ideas of one way of playing:
http://www.youtube.com/watch?v=ZfB3x4eOAHY