I seldom bother with splitting a carcass through the backbone. If I've shot something in the scrub I am generally reluctant to carry more than I have to so I generally just cut all the meat off the skeleton. However if I want chops, for instance, then I might split the backbone.
An expert can make a fairly good job of this with a cleaver. I believe that a heavy, sharp cleaver is best. I would use the portion of the blade closest to the handle to chop with, and just raise it a short distance each time to try to achieve maximum accuracy. But a cleaver can leave bone chips behind, and it is easy to go off track and cut off centre.
A proper meatsaw is a good tool for the job. I've also cleaned up a woodsaw and used it with satisfactory results.
The carcass should be hanging from a sturdy support and be securely hooked or tied. It would be a pity to make the final cut only to have one or both halves fall to the dirty ground.
Recently I helped an acquaintance butcher a sheep. We wanted chops so the backbone had to be split. This time I used a ten inch machete. While I could have used the machete like a cleaver (and I actually did this sometimes), I simply held it in place and 'batoned' it down the spine using a heavy stick. I was delighted with the results. Here is a picture which might help to explain what was done:
The ribs also have to be separated down the brisket. This was easily achieved with the machete.
I didn't want chops with the full rib attached, so I cut through the ribs. I found that a well placed blow with the machete did the job nicely. However, this did create a few sharp points and chips as the bone shattered.... so I had to clean these up.
The ribs were delicious barbequed.