At least, in my unit, it seems the fab only did the SMD soldering and used it to solder even through-hole components, but this results in sub-optimal solders:

So my advice is to solder them properly:

In my case, the new HDMI connector will sit on top of the DP connector, with the flat side facing down:

So, to be able to insert the HDMI cable without problems, I sanded/filed the bent edge of the DP connector because it was a little bit taller than the HDMI connector sheet.

It's just a tiny bit, until you feel there is no down step when trying to slide your finger nail from the DP housing into the HDMI housing.

Depending on your device and HDMI connector YMMV.

WARNING!:
If possible, use a location that blocks the use of both DP and HDMI connectors (as shown), otherwise add a label or something as a warning. Using both will short DP and HDMI sources together, and could damage some devices. You've been warned!.

Cut the panel according to the desired mounting position:

It is hard metal, so do some holes if you want to save time before the final filing work.

A bare HDMI connector can be used, but I think it is much easier to buy a breakout board to do the mod.

In my case, this board needed to be adapted to fit inside the housing:

At right, the original breakout board, at left, the board after cutting the unwanted parts.

I did the left side by filing, but could be done with sand paper or with a knife.

For the right side, i used my cutting pliers to cut the corner and then filed for the final touch.

Be careful not to remove too much (or you may cut some of the traces), in my board, the left side could be removed safely up to the point shown (the left shield-board ground plane connection was lost, but it is not needed).

These are the required signals from the DP connector:

Here you can see the signals needed from the display port connector, and the corresponding signal and pin for the HDMI connector.
The wires shown at left are not in the original product, I didn't take any picture before soldering the wires..

WARNING - DISCLAIMER:
This wiring is based on a fully tested device, so it should be correct (let me know if you find something wrong), but I accept no responsibility for any device damaged, you should check and double check your wiring using the official pinouts and documentation provided by VESA.

Some signals could be taken from the DP connector, but it is way easier to take them from far away in the PCB, this way we have more room to put cables and (if done properly) we can avoid unwanted bridges:

HDMI signals:

• In green: The Lane signals (TMDS for HDMI) must be taken from capacitors side connected to the converter, not the DP connector, because DP video signals are AC coupled, but HDMI must be DC coupled.
• In yellow: These are the DDC data communication signals needed to identify the monitor.
• In pink: This is the signal to detect the monitor presence (HP DETECT, pin 19).
• In blue: Ground.
• In orange (Optional): This signal (and the trace cut) are not needed by the HDMI, but this is an extra mod to fix the DP compliance of this device. According to the standard, this signal must have a 100K resistor, not be connected directly to 3.3V, so I cutted the trace and added the resistor between 3.3V and DP CONFIG1 (pin 13). For now this mod remains untested, I don't have any DP++ source to test it.

It should look something like this:

The image shows the added resistor between 3.3V and DP CONFIG1, the lanes wiring at left, the ground signal cable and the DDC data cables.

There is a missing cable in the image, the HP DETECT, pin 19, I took the picture before adding that cable.

The wiring should look something like this:

I did the wiring after soldering the breakout in place (more on that later), but now, I think it is better to solder all the wiring to the breakout before tying it down.

All the wiring comes from bellow, because the space from the pcb breakout to the metal housing is quite small.

But there is enough space to do the GND wiring on top.

Use a short wire for GND, and connect also the connector housing to this GND or other housings (see next step).

Notes for TMDS signal wiring:

• Keep them as short as possible, but don't go crazy about it, it just works as shown (Tested up to 1080p @72Hz).
• It is more important to have all the signals with the same wire length.

For the rest of the wiring there are no special requirements.

Because the HDMI connector must be able to resist quite a bit of mechanical stress when plugging-unplugging the cable or moving it around, it must be strongly tied somewhere, this is how I did it:

Two points:

• At right: using a bent piece of wire, and adding lots of solder to join it with the USB connector shield.
• At left: welding together the HDMI and DP housings.

Flux is recommended for these solders.

I also recommend to add a little bit of electrical tape to the part of the metal housing facing the breakout board, to avoid any possible shorts between the HDMI breakout board and the top metal housing.

This should be the final result: