Sounds like there is a problem in relaxing your left arm / shoulder.
I think you should try doing single arm chi sau just on the left arm , and just generally doing a lot more punching of the focus mitts /pads on only that left arm.
Don't worry about it too much , with me its the other way round , my left is faster than the right , although my right is more coordinated.
A lot of people would have the same problem whether due to a past injury or just carrying tension on that side. It might fix itself up or it might not , don't be too concerned .
Its not as if when you have to use it on some low life that they will be saying " Dude you hit like a truck , but that left one was a bit slow ".
We are not perfectly built machines , we have to work with what we
Probably if you examined yourself closely you would find that maybe one of your ears is larger than the other , or your feet what ever , except for some blessed individuals few of us are physically perfect.
See if you can even up the punching speed of your arms , but don't become obsessed by it. I've tried pretty much everthing , and one of mine is still faster than the other.
Don't train for speed, train for smoothness.
If you train for speed, many times your movements will be jerky, and as you get older you will lose speed.
But if you relax and train for smoothness, then speed will come naturally and will continue into old age.
Like Mook said, dan chi on the left side. I would also say SNT with extra emphasis on that side.
I'm right handed but many times my left hits harder because I have less force to give up on that side