How to socket 28-pin DIPs?
If you want to put DIP packages into milled sockets you have to be conscious of the side forces from the package leadframe.
Milled sockets such as you are using are NOT designed to have large side forces on the socket and your DIP package leadframe is bent out at an angle as shown below (typically 5-15 degrees):



For milled sockets your DIP package should ideally be able to stand with the package lead pins in the center of the sockets without having to put side pressure on the DIP package pins. 
For hand insertion there are a bunch of creative leadforming jigs (from simple to complex) that will ensure the leads are normal to the body and at the right width: 

 

I usually just hand bend on a flat hard surface. You just have to be careful to bend the leads right at the shoulder and not just bend the lower leg.

some open frame slide contact IC sockets can actually withstand considerable side force without popping out, but they have a high shoulder to surround the leadframe pins:



...and not designed for continuous re-insertion.