Possibly the oil injection system is failing.
It does sort of look like the mixture is on the rich side by the looks of the plug. That could be caused by oil intrusion too, most common would be leaking valve stem seals (if this type engine uses those). But that amount of carbon as shown in the photo wouldn’t normally affect the plug performance. If the carbon is bridging the gap, then it definitely will affect perforance. But the gap is completely open it appears. So it is hard to understand how replacing that plug could have helped the symptom.
The gap in that plug looks to be a little on the wide side. But the recommended gap varies car to car. Good idea to check it against the car’s specs in any event. And make sure the plug part number is one recommended in the owners manual.
There have been some complaints here about plugs with 4 electrodes. If any of the plugs involved had 4 electrodes (rather than the single electrode in the photo), good idea to be suspicious of those.
George, these engines don’t use traditional valves. I think you’d enjoy the link I posted earlier.
These engines are both ingenious and unique. One common characteristic of them when the apex seals get worn is oil ingestion manifesting itself as sparkplug fouling. While 200 miles is extremely short, I have an uneasy suspicion that that’s what’s going on here.
What I don’t know is how those who’ve immersed themselves in these engines deal with these issues. I simply don’t have the experience to know. I still hope the OP visits some RX8 forums and/or searches out some sites specific to this engine to learn more about it. I’m not sure the solution to the problem is going to be found with the same approaches used on conventional reciprocating engines.
I could be wrong. It could be simply rich operation.
I did take a good look at the configuration of the sparkplug. It appeared to me to be an unusual design with a segmented “wall” around the center electrode, but I could have sworn I saw a single ground electrode. Perhaps that “wall” has something to do with the cylinder turbulence and flame propagation.
I wish I knew more about these engines. I’d really like to help the OP. I feel so… lacking.
Also, for those who might be interested, there was an episode of “wheeler dealer” where they bought one and Ed explains how the engine works and how to test it/etc. Pretty interesting.
I used to work for a multi-line dealer and one of their lines was Mazda. While I didn’t get too deep into that make myself a friend and co-worker who worked alongside me did as he was the resident Mazda guy. War story swapping every day is common in the trade… 
When problems did occur with the Rotary engines they were really never repaired due to costs. Most problem cars went away as a trade-in to be wholesaled or sold in the classifieds as the owners had no desire to dive that deep financially into fixing one of them.
Back in the day my older brother bought a used RX-3 (yes, a 3!).
Abandoned a nice Toyota when the clutch went out (smart move, but another story).
Within a couple of weeks it got harder and harder to start.
Pulled the plugs. Fouled and oil soaked.
Replaced plugs. Ran OK for a week. Plugs soaked again.
Some mechanic (memory foggy now) suggested kerosene in one plug hole until it ran out the other (two plugs per rotor) then crank with the plugs out to flush out the excess oil.
Wound up doing this weekly until he ditched the mother-father (tip o’ the hat to Redd Foxx).