Obviously I cannot comment on the quality of your application documents even after somebody assumingly knowledgable has reviewed them - but in any case I would submit your application directly via the consulting firms websites. Even though McKinsey does not explicitly favor those applications coming in directly via the direct website, it eliminates an intermediate (for the consulting firm more or less useless) step and reduces process time and risk.
Looking at your situation from a slightly distant point of view, it doesn't sound that you really stand out so much from the crowd of other applications. That's already an issue in "good" economic times, even more so at the moment of COVID-19.
Since recruiting activities are starting to slow down, I am afraid that the "classical" approach of submitting documents and passively waiting a reply will work less and less for non-experienced hires that are not in severe demand at the moment.
The most secure way to getting your interview invitation is as usual networking your way into your target firms. The more senior that person referring you internally, the more secure is your interview invitation if right now (please note that I am not referring to a job offer, I am talking only about being invited to interviews - however I expect the bar to be rising).
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