Your proposed equation looks wrong, Dave. Check it against the recession speeds given by Morgan's calculator. The link is in my sig. Be sure to enter the usual parameters 0.27, 0.73, and 71 for present matter fraction, lambda fraction, and hubble rate.
When I do that and put in z=10, I get that the recession speed is 2.28 c.
You would have the recession speed be ln(11) c. That is 2.40 instead of 2.28. Well that is not too bad!
Now when I put in z=1090, I get that the recession speed is 3.3.
But you would have it be be ln(1091) = 7.0. That is way off. Either Morgan's calculator, or your formula, or both must be being pushed too far.
Maybe your formula is all right as a rough approximation as long as you just apply it to small redshifts, and will therefore suit your purposes (depending on how you intend to use it.) But as a rule I don't think it works. The relation between recession speed and redshift is not that simple.
Part of your equation is right though. Hubble law does say v = Hd. Hubble law does not talk directly about redshift. It gives the recession speed.