It is a very well known problem:
https://www.reddit.com/r/MechanicalKeyboards/comments/2l1xqg/guide_fixing_grindingsticking_thick_pbt_keycaps/I noticed the same problem a while back when I bought Vortex keycaps that are also made with thick PBT for a Filco. Unfortunately changing to cherry stabilizers on that board will not be an easy task because the plate does not have the proper cutouts for cherry stabilizers. If you don't like grinding the keycaps your options are to either get Tao Hao keycaps, that have thin PBT or to get a different keyboard with cherry stabilizers. If you don't like the colors available with the Tao Hao keycaps, there is a set:
http://www.wasdkeyboards.com/index.php/products/keycap-set/doubleshot-pbt-104-key-cherry-mx-keycap-set-black-slate.html that is also Tao Hao double shot black with white legends. Ducky Shine 3 TKL or Zero have clipped cherry stabilizers, the same that are used on your Ducky Shine 4. Max Keyboard Blackbird TKL also uses clipped cherry stabilizers. If you don't mind a bit of soldering you can get any keyboard with cherry stabilizers and clip the stabilizers yourself, otherwise cherry stabilizers make those keys too mushy when bottoming. You only need to desolder and solder back the switches that have stabilizers on them. That is currently what I'm doing, and a relatively cheap option is to get iKBC C87 or G87. G87 are available on ebay from a respectable seller in the community
http://stores.ebay.com/esportsgamingequipments/. I will write a review shortly, I'm waiting for my package to arrive. They might also have clipped cherry stabilizers, but I couldn't find information about it. I also use Ducky dyesubs and I love them. I would recommend for you to stick with your keycaps, don't mess them up by grinding them, and just get a different keyboard. I personally think Ducky dyesubs are among the highest quality keycaps available, only rivaled by Imsto. Those, however, use cherry profile, and if you ever decide to use o-rings the Imsto would have a problem with them, while the Ducky work perfectly with o-rings.