The events in questions are no longer than one kilometer and have a gradient that fluctuates between 7% and 13%.
First thing to do would be to get some data about your max power outputs over different gradients & conditions. So you'll want to know what you can sustain over a 10% 3 km climb, or a 10k climb at 5%. You'll also need to know how this fits into different length rides - you'll be able to output a higher average over 15 km than you would over 30 km.
The relationship between power, gradient, cadence, gear and speed is complex. Increasing power will cause your cadence to rise, thus speeding you up. The steeper the gradient, the more resistance there will be, so it'll take more power to remain at a steady cadence (in the same gear).
Dividing your power by your weight will give you a watts/kg rating which is useful.
Once you know all this data, you'll be able to look at a hill and know that, all else being equal, you'll give your best performance if you maintain, say, 4 w/kg for the climb. You can then use your powermeter output to adjust your effort accordingly.
Edit: Mind you, if I understand the event description correctly, I suspect that over that sort of distance you are best off just pushing on the pedals as hard as you can.
In your previous question hill climb tt pacing strategy for short steep hills?, I got the idea that you know where the races will be and can practice on those hills.
If that's not the case, find some other hills to practice on.
Do practice rides with the power meter.
Firstly, by using the meter, you will develop more power. If you want something to change then measure it. Make sure you follow a proper training and recovery schedule.
Next, you will learn how it feels, at a given power level. And how it feels when you're ready to bonk. Maybe you'll decide you don't like to have the thing telling you what to do, or maybe it will spur you on. But you need to learn to hear what your body is saying; it doesn't always produce the same feelings and performance every day.
And finally, do some tests and keep records. No one can definitively tell you the best way for you to race. Only you (or a personal coach) can discover that. And different people are ... different. That's why sport is so unpredictable.
Tests you might try are variations of
Choose some different power levels or different speeds and see how you go. What happens if you do the same hill with 5% more power? Does it work, or do you fade out? What happens if you try at one speed, then try 1kph faster?
Keep reading the various blogs related to power meters and climbing. Affordable power meters are new and we are still learning how to use them best. Remember that you are your own coach, so set out a training plan for the athlete you are coaching (you). Make sure every session has a goal, and give your athlete some training variation. And then come back to the same test, to see what progress is being made. There are more books and blogs on this topic too :-)
I would recommend using your power data to make sure you aren't going too hard out of the gate, like with any time trial. Try to keep your power in the Threshold-VO2 max range, with a high cadence, until you're within striking distance and then drop the hammer to the finish line. More on determining power levels here.
This assumes you know how long you can hold a sustained AC level (aerobic capacity) effort. I would try to pace it so that you are ramping up your power into the finish, not a big burst at 200 meters out and then a gradual taper in.
It really depends on the character of the climbs, I think some pre-riding of the course would be as, if not more, beneficial than power data for such short efforts.