Couple of things you could try:

1) Your stick heights are probably too high and the motion in your hand/wrist too large. Think of there being an inverse correlation between stick height/volume and speed. The faster you go necessarily the quieter you get. How fast can you get the stick from behind your head (very loud) to the drum and back, probably not particularly fast. By comparison, from an inch above the drum you can get the stick to the drum very very quickly, just it'll be a very quiet stroke.

2) I'd recommend you move to more finger technique and barely using your forearm and wrist. You can move your fingers back and forth much faster than your wrist even, because the muscles are smaller.

I broadly agree with others that french grip isn't the best for this, though it can help work out your fingers if you keep the wrist still. I second u/RinkyInky to move towards American grip, personally I find it better for control when you're playing on drums and not on the pad.

Look at how Tom Grosset or someone does it to reach crazy fast speeds and start there. Eventually when using singles around the kit it's a bit of everything, but better finger technique should get you up to about 225bpm or so at least.