I have the "shiny" spots on mine as well. I bought RaggTopp cleaner and fabric protector and cleaned/ conditioned it last week. The tops looks good and it seems to have lessened the shiny spots but they are still noticeable in the sun. I just bought the car and have been going through detailing it, so I'll keep at the top and hopefully over time properly cleaning it, it will become "renewed".

Cleaning the top: Following the instructions on the bottle, I wet the top, sprayed on the cleaner, worked it in really well with a sponge (circular scrubbing motion first, then brushed it front to rear like the owners manual suggests), hosed it clean, let it completely dry overnight in the garage.
Fabric Protection: The next day I took old sheets and put down the windows, popped the front and rear of the top and secured the sheets under the top and over the windows and top of the windshield and closed up everything to protect the paint and glass from overspray. I then sprayed down the top with the protector per the instructions (three coats for first application). Make sure to wipe off the rear window (or anything that is not the top that got some on it) between coats b/c the fabric protector is greasy when wet and might not come off the window easily when dry. Let it completely dry (says 48hrs) and water should then bead up on it when it gets wet. I finished by running a lint roller over it to get all the loose lint off.

Good Luck!