You can look at lighting equipment, where the carabiners they use are smaller. These carabiners are intended to be used in conjunction with a steel safety cable as a failsafe, should the lighting fixture come off its intended attachment area, so it should be able to take quite a fair bit of weight.
These carabiners are still too thick to go through the camera eyelets (doubt you will find a carabiner thin enough to do that), but you can figure out some way of attachment from the eyelet to the carabiner, one carabiner to one eyelet. Then find some way of making the ID strap compatible to these carabiners, such that you can quick release via the two carabiners.
As for where to purchase them, I'm not too sure, but places that sell professional lighting should carry these, so check the Sim Lim Tower area.