Need help cleaning my waveforms on a simple half-bridge

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I'm trying yo build a very simple and low power half bridge smps.
I don't really have a schematic but, it's just a pwm signal theat is feed in 2 high speed opto couplers (6n317).
The mosfet driving side is powered by two 14v isolated power supplyes, with the out of the opto couplets going trough a not gate and then to two tc4420 mosfet drivers. I have 50ohms between them and the gates.

The mosfets are a pair of irfp260 and the voltage being switched is just 12v and is limited at about 5A

The transformer is a small ferite core wound bifilar 10:10.

The whole thing works but under moderate load there is some ringing.

Gate waveforms without main power.

Yellow is low side mosfet and blue is the midpoint between the mosfets, under no load:

Same under small load (12v halogen light bulb):

I did try to add rc snubbers on the mosfets and ultra fast diodes also paralel to the mosfets, but the ringing is still there.
Will do so later. I will try to shorten as much as I can some connections and give the rc snubbers another try, then I'll post more waveforms and the exact values I used.

The secondary waveforms look very close to the primary. They look very strongly coupled.
The waveforms from the first post are from the primary side.

One thing I don't understand, when the duty cycle is close to 100% (50% per phase) the transformer is actively driven almost all the time, but at lower duty cycles when both the fets are off it's normal to have the transformer going into flyback mode at the fets turn off, and using snubbers is the proper way to dampen the oscillations?
Ok so

Low duty cicle, unloaded and no snubbers, yellow is the low side fet gate, blue is the midpoint between the fets:

Now loaded with 3.3 ohms on the secondary:
Same, zoomed in a bit:

Now with a 13ohm 1uF snubber across each fet drain source:

And on this the blue is the waveform on the secondary:

And this is how the whole contraption looks like....

The two capacitors that from the other leg of the bridge are 680uF 200v, and there is no series capacitor with the transformer.
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