Do you mean something like this:
HDMI Vertical Mount

Looks good.

Did you find similar Type C or Type D connectors as well?

http://en.wikipedia.org/wiki/HDMI#mediaviewer/File:HDMI_Connector.jpg

All i found for type D is the male version. Still searching...

sadly i couldn't find small ones (C or D).

checked on Digikey, Farnell, Mouser, AVNET.
and Manufactures: Molex, Samtech

i think the reason is that for TV's and Monitors you need sometimes Vertical Mount HDMI and they use only the A Type.

Just for reference, most HDMI receptacles are 90° (aka RA).

The ones you are looking for are called straight or vertical, but for the Beta, they seem to be of little use.
(what would be the purpose of having HDMI receptacles pointing to the front of the camera?)

I've investigated another kind of HDMI receptacles, labeled V-RA (vertical, right angle), which seem to be suitable for the Beta Shields.

http://uk.farnell.com/te-connectivity/2007435-1/hdmi-buchse-fahne-tht/dp/1816577?ost=1816577
http://www.mouser.at/ProductDetail/Kycon/KDMIX-SL1-NS-WS-B15/?qs=%2fha2pyFadugN3I2uwon6LNmzXz1eBvK27BO1w0I%2f5nWq%252b6x1HD28Sx2VhuG%2f3e%252bx

One idea from the ergonomics work-group is to make the HDMI shield wider than the rest of the boards and have the connectors point towards the back of the camera.

Sounds impractical to me, as both, the planned Beta Board as well as the MicroZed have connectors on the sides, so they are likely to be blocked by those backward facing receptacles.

it doesn't really fit here but as a small side note:
i stumbled over HDMI connector form Neutrik:

https://www.neutrik.com/en/neutrik/products/multimedia-connectors/hdmi

In T93#16331, @christophvarga wrote:

it doesn't really fit here but as a small side note:
i stumbled over HDMI connector form Neutrik:

https://www.neutrik.com/en/neutrik/products/multimedia-connectors/hdmi

interesting, thanks.

Expensive though as expected: https://octopart.com/search?q=NKHDMI