In theory pry it out and put a new one in (from the outside).
If you still have the original one it will be less flexible than a new one.
A bit of soap makes is easier to put the new one in.

The W126 has an upright tank (against the rear seat) and the filler neck is only slightly higher than the top of the tank. It is very important not to overfill the tank.

Fuel should not gush out if you remove the cap, unless you park on a very steep incline.
It sounds like you overfill the tank. These tanks have a overfill protection, a small tank inside with small holes in it, this prevents overfilling. If you fill the tank completely, wait a few seconds, and top it up again, you bypass this protection and overfill the tank.

Rob