Use the wood it is fine. In some regions they don't use strapping at all (for 16 O.C. not 24) but I can't help thinking that they would get some cracking after a while. Some pointers: Snap your chalk lines and put up your strapping. Use only one nail per joist at first and use shiny common nails. This way you will be able to tap the high ones down and put in your shims. If the joists aren't too radically out of plane you might be able to flatten things well enough by eyeballing the high spots instead of running all those strings. When you are done then put the second nail in each joist to secure things. This should at least be a ring nail so it won't slip later.