The Makita and C3D collets are not attached to the collet nut. The collet is squeezed up an inclined plane to tighten the X pattern on the collet by the collet nut. When you loosen the only thing that makes the collet relax and spread to come down t he inclined plane is the spring in t he collet. Since yours is stuck and you have heated and lubed it would be to put the collet nut on so the threads of the router shaft are covered and tap with a plastic handled screw driver. Do not beat on it with a hammer or steel object. The hope is the vibrations makes the collet slip down and fall out.
If you get the collet and bit out of the router than clean it with brake cleaner or other degreaser. The collet should be dry as a bone with no lube. Since your bit has been stuck you will be tempted to lubricate it but that will lead to bit slippage. You should replace that collet if you can get it out.
Be sure to leave t he collet nut loose but covering the threads.