I would argue that hiring a DP wasn’t (fundamentally) the mistake. Not conveying things like time base (24p) and overall vision... those are the mistakes, and you’ve already acknowledged that.
Hiring that particular DP may have been questionable, but only in hindsight. Lighting that is flat and dull, poorly-recorded sound, poorly-framed shots, a glaring and obvious C-stand in the background... all signs of a DP who isn’t paying attention. And the lesson here is that these things can be corrected on set. The director should be sitting at a monitor, wearing headphones fed by the primary audio recorder. It’s your job to see and hear what’s being recorded and to speak up if it doesn’t meet expectations.
I’m not sure the solution is just to do it yourself, because that doesn’t give you any more experience in communicating effectively to a DP. You know what went wrong, and that gives you a great place to eliminate those challenges on the next short. A thorough pre-pro meeting can move most of that conversation away from the set, too. It’s there that you look over the storyboard and clarify tech specs (“to be shot at 1080p24” or “to be shot at 4K, 24p”) and convey your visual taste (do you want contrasty, dramatic lighting, or lower-contrast/desaturated, or something else?).
The good news is that you’ve got all this from your last short, so going into the next one should be much smoother.