Center cutting or box hearting timbers usually starts with the timbers are 5"x5" or greater. If the braces are 3"x5" then they usually aren't center cut/boxed heart.
In an oak log if you make one large cant and then cut it down the middle to make two each one could bow due to stress in the log.
If it was me, I'd make one center cut/boxed heart timber, if it is going to be larger than 5"x5".
Checks or surface splits are part of timber framing....
I've never used sweet gum so I can't help you with that....
