None of that "opening up" will do for my game dealer who wants micro surgery to leave as little exposed as possible, especially between the haunches. Not one for suspending a deer, you have to carry rig for the bigger deer and I think most people carry too much as it is. Exposing the windpipe from sternum to under it's chin, strip the oesophagus of meat at the base, roll the remainder forward to as far as you can, cut off and tie. The meat that "balls up" at the end acts as a stop for the knot you've just tied. Cut the windpipe off near the sternum and move onto the gralloch.
Once opened up which only needs to be micro surgery style, with the animal on its left side, holding the ribcage, cut around this side of the diaphragm, roll the animal onto it's right side, holding the ribcage again, cut around this side of the diaphragm. Once done, put your knife down, and with both hand, reach in and grab the heart/lungs (it helps with long sleeved vet style gloves with a latex glove over the top to avoid getting blood and ticks on you). Even on the bigger fallow and sika stags (don't know about red), by using the ribcage as a leverage point for your forearms, everything including the remains of the windpipe and oesophagus can be pulled out relatively easily. The liver remains towards the top of the gralloch which can be taken along with any other offal without it touching the floor and placed on a small sheet of plastic. The rear pipe can be stripped, cut and tied off for removal at the larder for ease. The gralloch can be put aside or disposed of as usual.
None of the edible parts of the carcass has touched the ground as yet, but if you want to drain the open cavity by turning the animal, rear legs spread, you can. This can however, allow the exposed neck and the edge of the opened cavity to come into contact with the ground. If you do not want anything coming into contact with the ground, you can clean out the majority with one hand after removing a latex glove. Remove the latex glove from the other hand, pick up the liver with it and fold the long sleeved glove over it for a ready made and clean offal bag. Place any other offal into the same bag and jobs a good un.
Doesn't take long, no chance of any contamination, either offal or carcass. A did see a tip offered on a video some time ago, where the front legs are placed over the top of the animals neck which aids the carcass shape once rigor mortis sets in, so I usually do so. It sets the shoulders in an upwards position whilst hanging and seems to work.
I guess the only disadvantage of my method is the bending over which shouldn't be for too long, and the use of the plastic gloves which are classed as single use, by I use them to both keep myself clean and for use as an offal bag. The extra expense of these gloves are more than offset by a payment the dealer makes for it. The advantage is nothing extra to carry albeit a few pairs of plastic gloves, limited chance of contamination from an overly exposed carcass and speed of processing as apposed to finding a suitable location and getting out the kit for suspending larger animals.
I'm lucky in so much as 95% of the time, I can get directly to where the animal has fallen with an ATV, but if it needs to be dragged at all, a sled can be used.