After removing the shield, take out (and save, just in case you lose a part) the sim eject mechanism parts, and then take an exacto knife, and slide it under the sim card reader. Melt the first solder joint on the reader, sliding the knife in between the pad and the leg of the reader to prevent it from soldering itself back on.

Proceed with the desoldering, whilst advancing with the knife further under the reader. Finally, once all 6 legs are done, do the same with the two remaining legs, being extra careful with the left one (the right being ground). After this, the reader should come off without further prying. If not, check for intact solder joints.

Better pictures are welcomed, add yours if you attempt this.