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None of the predefined monthly summary reports are going to have exactly what you are interested in. Instead, I would recommend that you define a new monthly report that uses ValueWhenMaximumOrMinimum. Some examples of how to use that are in the documentation and in the example file PurchAirTables.idf (and other example files as well). In your case you will want to have Cooling:Electricity with Maximum aggregation type and then list each end use with the ValueWhenMaximumOrMinimum aggregation type.
As far as daily consumption for the peak day, I cannot think of any way to do that except to save individual output:variables and do some post processing to figure out the peak day for cooling demand. You might be able to use Reporting Frequency set to Daily to cut down on the data collected. If you are running each simulation and doing post processing of the outputs right after each, you can always delete files at that point to reduce data storage.
If others have been interested in having a special Aggregation Type related to summing one variable over a day when another variable is at its maximum or minimum, please add a comment and I can post a new issue.