Good question for a not-uncommon situation.
Firstly, check your local codes to see if unvented attics are permitted. If so, I would keep the blown-in fiberglass insulation and additionally foam or otherwise insulate the underside of the roof deck. This will give you a semi-conditioned attic space and, combined with your blown-in fiberglass, a high overall R-value. A semi-conditioned attic space will allow your ductwork to work more efficiently by reducing the temperature gradient between the inside and the outside of the ducts.
You will also benefit by making sure that the ceiling is sealed around all the penetrations. (This will have less but still positive impact if you are able to seal the attic and insulate at the roofline.) If you also have hollow walls that are open to the attic, make sure the tops are capped off and air sealed, and then insulated over top. The key is to stop unintentional airflow in and out of the condtioned space and also make sure that the insulation is continuous and continuously touching the air barrier.
If you are unable to seal the attic, still seal around all the ceiling penetrations and any open walls and make sure your insulation barrier is in contact with your air barrier. Then, depending upon the R-value of your blown-in insulation, you can always add more. You can also add batts of recycled cotton insulation over top the blown-in insulation if the joists are tall enough to support it without compressing the existing insulation. Also make sure the ductwork is sealed with mastic at all connections and insulated. If it is relatively new flexduct, it should be continuous and have built-in insulation.
You could remove the blown-in fiberglass, but it seems like a waste of resources and insulation value, given that it is only a few years old. By sealing the penetrations and making sure your ductwork is sealed, you minimize the opportunity for the fibers to get into your airspace. Always make sure you are working with a respirator mask when you are disturbing the fiberglass in the attic.
If you are considering foaming the ceiling instead of the roofline, make sure the recessed lights are insulation contact-rated (IC-rated) and get a local foam insulation installer to review the entire situation before you go to the effort of removing your fiberglass.
Finally, if you are unable to seal the attic, an attic fan could be of help in the summer. Be cautious, however, in making sure all ceiling penetrations are sealed and that there is adequate gable or other venting to supply makeup air to the attic fan. Otherwise, the negative pressure in the attic created by the fan will cause the attic to suck the air conditioning out of the house through the penetrations and hollow walls, creating the opposite effect that you desire.
Good luck on reducing those air conditioning and heating bills.