The "backing off" value is the "D" constant in the PID term. If you're still at 95% when it hits 225F then that means that it is approaching so slowly that either:
A) the "I" sum has built up so much that the the device is powering through your setpoint
B) the "D" constant is too low so the slow temperature change doesn't let it back off enough
Next time you're logged in to heatermeter on startup, press the "P" key on your keyboard to activate the "PID Internals" graph. It will show you the current proportions that the P, I, and D values are contributing to the output. When you hit your setpoint P will be 0%, your "I" will be a large value, and then the "D" should be a negative large value. If you want them to perfectly balance out, you can take the "I" value and divide it by the "delta T" value, which is the change in temperature, and set your "D" constant in settings to whatever that number is. For example, if your "I" is 95% and the "delta T" is 10, then set your D constant to 9.5.
You might find that that D value is too high for normal use, which would mean you'd want to decrease your "I" constant so it wouldn't build up so large a sum so fast. If you're running "Fan startup max" not at 100%, because that slows the initial approach to the setpoint, it could be allowing your I sum to get too large as well because the I sum is attempting to compensate for the grill not heating up quickly enough.
With the default constants on my BGE, my output goes to 0%-20% about 5-10 degrees below the setpoint because it is usually approaching so quickly that the "D" constant shuts the whole thing down well before it even gets there.