I had the same problem when I purchased our 55 plate CVT back in September, the Honda specialist I took it to told me the Honda recommended procedure was 2 flushes and then a final fill using ONLY Honda CVT-F fluid as Jocko has said. I also asked them to add a syringe of Xado EX-120 as a ‘belt and braces’ approach, it has been faultless since then.
I would suggest if the fluid was reported ‘black’ it was either very old or the incorrect type and a change on it’s own would not be enough to sort it, the only way is to follow the Honda recommended method and see how you go.
It’s not just high mileage that requires the fluid to be changed, as low mileage possibly causes more problems with condensation forming in the gearbox which I believe is one cause of the stuttering. Our car will be lucky if it does 3k per year and I will have it flushed and refilled every 2 years, to hopefully prevent any further problems.
EDIT
Just did a bit of Googling on Dr. Tranny and it specifically states it is for use with ATF and Torque Converter transmissions, if it were me I would be flushing that out with several flushes of the correct fluid ASAP.