The hill is 0.8km long with an average gradient of 13%. My cadence on my 46t-36t 11-25t 9 speed gear ratio starts at 80rpm and rapidly dips to 40 rpm. Is there a way to calculate what gear ratio is best for me to move to?
Aside from pacing better, if your cadence drops to 40rpm for too long and you are in your lowest gear at maximal effort for the expected duration, then you could probably use at least a gear 2/3rds or less than you currently have so you are likely to be able to sustain closer to 60rpm.
That's possibly not feasible on your bike, but perhaps a 29 rear cog at least would help get cadence up a bit higher. Being stuck at 40rpm is probably (but not certainly) compromising your ability to generate maximal power for the duration. Depends on how often or how crucial this climb is to your overall performance goals. If it's not that important and you only deal with such climbs rarely, then making such a gear change probably isn't worth it.
Of course if you are carrying extra dead weight, then working to trim down can also help since steep climbing speed is all but linear with your power to weight ratio. At least a power meter can provide additional insight into your overall metabolic energy demand from training so that you can manage diet and medium term energy balance for sustainable/sensible weight loss.
The short and most direct answer to your question is to use your power meter to pace your ride optimally and Alex Simmons, who has given another answer to your question, was too modest to mention that he is an expert in this and has developed one of the most sophisticated power pacing models for variable conditions.
A longer answer is, to paraphrase Prof. Jim Martin at the University of Utah, cycling fast is about maximizing the power you can make, and minimizing the power you must make. You can use a power meter to address both of these.
Obviously, you can use a power meter to train so that you can maximize the power you can make. I will presume that you are already familiar with some of the training methods.
Less well-known is that you can use a power meter to identify and estimate the sources of drag and inefficiencies that consume power so that you can (sometimes) minimize them. Proper pacing is in this category, as optimal pacing can help you get lower overall times on the same overall energy expenditure. In addition, you may be able to use a power meter to estimate rolling resistance losses either in your tires/tubes or drive train to make better choices about equipment. Rolling resistance from your tires and tubes scales exactly like hill slope, so a decrease (or increase) of .001 in your coefficient of rolling resistance (Crr) is exactly like decreasing (or increasing) your slope by .001, or 0.1%. This may sound small but in a race where seconds matter the difference between winning and finishing off the podium can be smaller than the difference between racing up a hill with an average slope of 8.1% and 8.2%. Your speed on this particular hillclimb is low but on other hills your speed may be high enough to warrant looking at aerodyanmic drag, which you can also estimate with appropriate field tests using an accurate and precise power meter.
And, although not strictly something that requires a power meter, you can use speed and cadence to estimate gear usage throughout your climb to see not only which gears you used but also when you changed gears. You can see an example of how that is done here, which is an analysis of power, cadence, crank torque, and gear usage during a hill climb. For example, here is the gear usage during this 15-minute long hill climb race, with dotted red lines marking 30-second long intervals, which are numbered in red:
Then, using power data, you can calculate crank torque and examine the combinations of cadence and torque used to see whether you "bogged down" or were "lugging". Here is an example, with each point in the plot keyed to the numbered 30-second intervals identified in the previous plot:
All of these latter uses, however, require high quality data from your power meter over a wide range of power, cadence, and torque. Because changing bilateral asymmetry in pedaling is common, especially with cadence, torque, and fatigue, the Stages is not an ideal platform for these latter analyses. However, you may be able to get an indication (though not conclusive proof) from your race data whether this is a likely problem. Since you're using Golden Cheetah, you can click on the "Aerolab" tab and see whether the virtual elevation estimated from your speed and power matches up well with the elevation recorded from the altimeter. You may have to "zoom in" on certain parts of the Aerolab plot to see areas of fit and misfit.