Before reducing log splits much more than that, I like to find out first how many bows are potentially in a stave. To do that, I take off all the bark and crudely chase the sapwood/heartwood to 1 or 2 rings above the one I want for the bow back. Then I use a pencil to trace the the grain down the center of the stave. Sometimes you'll find your line stays in the center of the log split, which means your original split ran true. Barring any flaws that you may want to avoid, you may in fact have 2 bows in the log split. Quite commonly, though, you'll find your pencil line runs diagonally across the log split. In that case, your original split had some runout and you may only have one bow in the log split. I like to find that out up front, since I don't want to split again only to create firewood. Also, my preference to bone out a log split that's only 7" wide is to bandsaw it into 2 staves rather than trying to re-split, since splits (again) don't always run true and trash the perimeter of the stave. If the log split doesn't have any runout and you lay your lines out and bandsaw carefully, you may even get 3 staves from that split.
Likewise, belly splits are tough to pull off cleanly, unless bandsawed. Unless the log split is unusually deep and wide at the bottom, I don't even bother with them. Belly splits get very narrow and the grain often meanders off the stave too much to get a bow from them.
