Design Ethernet capable board without RJ45 socket

Question

I have been tasked to design the schematics of a board of an ECU which provides 4-pin Ethernet on its 58 pins connector, for a 100Base-T implementation; I have been mandated the use of TI's DP83822 PHY(datasheet).
Application implementation in the datasheet shows the following, pg.104:

I have some (limited) experience with wiring up an Ethernet connection on a board, but never faced the request to have the differential pairs terminated on something that was not an RJ45 connector. Last time i used this connector, and I'm focusing on its schematic, pg.15:

From what i understand, I need to find the transformers to implement the magnetic part of the of the connections, with the center tap connected to the pull-up, and the filter; i also need to accommodate (somewhere?) the 75Ω termination resistors, and the CMC.
The only thing I can gauge from these schematics is the turn ratio of the transformer. How would i go about and find details on which magnetics to use? Is there any standard for this?
(Bonus question: can this actually be made to work at all?)

Additional info:
No details are given about the interconnection which is going to be placed after the ECU connector itself, but since target use of this port is "Diagnosis over IP" it can be reasonably supposed that it will connect to either a switch or directly to a PC, therefore i assume it will be a male RJ45 plug; est. cable length 40cm.
I have been told that they will make sure the cables carrying this signal are twisted pairs.
I was also told that no additional circuitry is allowed outside the ECU box.

Answer 1

Any standard Ethernet transformer intended for 10/100 Mbps operation should do.

Maybe you need one that is automotive rated in your specific case, so not entirely standard for normal use.

But otherwise, it makes no difference if the transformer is integrated into the connector or not, or if the connector is a standard 8P8C modular jack, or M8 connector or whatever custom you have.

So what you previously used is not really just a connector, it was a module that contains both the Ethernet transformer and the connector.

As long as the connector and wiring is good enough to pass Ethernet according to standards (which is of course anyway a requirement), it should work.

So itself it is not that important that the wires are twisted, it is more important that the Ethernet pair have correct impedance.