Merge separate audio ground signals
Assuming the "Full Bridge" to be absolutely true:  There are no grounds in the 4 pin connector that can be connected together - not galvanically nor capacitively. Probably in your player there are some resistors in series that have prevented the full short circuit and smoking in your tests. Instead of total disaster you fortunately got only a passive mixer. The reduced stereo effect proves that.

In theory you can find somewhere inside your player a proper ground and use it. Then you could use (a quess) L+ an R+ as the the signals.  Without a proper schematic there's no quarantee that you get the right filtering and the level setting resistors along. Probably you also must add 2 capacitors to cut the DC path. If thislike hack happens to be succesful, you will get about 6dB reduced signal level.

If you had a proper schematic, show it. Then someone here has a possiblity to provide a better solution than quesses. In theory if you tell the exact model of your player, someone can know what to do. But that's only theory.

Addendum after the insertion of the schematic:

It is stereo full bridge output. None of the four output wires are the ground. Both earplugs float between 2 hot outputs that have oppositely phased signals. The 15 Ohm resistors have prevented the smoke effects when you plugged a normal 3 wire connector.

In the audio signal path you see the capacitors C783 and C784. These and 2 others belong to output low pass filters that remove the hf from the pulsed audio. Those caps are connected to ground. Find that ground. It can be your headphone ground for 3 wire connection. 

The signal wires can be L- and R- (not R+ and L+ because the safety resistors are in minus wires . Those signals unfortunately have approximately +1 volt DC that must be blocked. So both of your headphone signal wires must have a hefty capacitor in series. In practice one capacitor would be enough if it is in the ground wire, plus pole towards the headphones. The capacitance must be big to prevent the reduction of the bass. Start with 470uF. That's calculated for 32 ohm earphones and 25 Hz -3dB. No need for more than 2V max voltage.

A little rational thinking is also here well placed. It's no good for any working equipment to get fixed, if it's not broken. Additionally the extra ground wire from there somewhere totally prevents others than you to operate this player properly. 

Seriously: get a 4 pole plug or a cable with such plug. Rewire your left and right earplugs to that cable. The connection is the original one, no extra wires and you also get the the full normal output power.

In the case you plan to connect something else than headphones to that connection, you must be extremely cautious. The hf removing filter assumes 32 ohm load. Higher load resistances give bad resonances.  Additionally the DC blocking capacitor must be in the signal wires.