Ethernet and passive PoE passthrough while taping in to PoE

[kristaps_r]

Hi,

My goal is to make device that passes through gigabit Ethernet and passive POE and at same time to use some energy from POE.
My idea is to use ETH transformer with ethernet ports on both sides, connect center taps of both ends and use bridge rectifiers to get power.

1. Does this look correct or I have to use double transformers?
2. Transformers usually include filter in one side. Could not find if they also are non symmetrical in case of winding current rating if I feed it from one side to other side center taps?
3. Probably there is correct way of tapping in to POE without transformer in series but keeping signal undisturbed?

 

[kristaps_r]

Here would be both options I am thinking of: