Since you do have a few days leeway, why not select a date when you reinforce the moon and let it have the most positive aspects possible?
In terms of timing on the day, try turning the chart so the most significant planets are above the horizon, not below.
Here ia a link to some general rules for election charts:
https://www.astrocollege.org/campus/libraries/General_Rules_For_Electional_Charts.pdf
The college application involves the 9th of higher learning, and the ascendent with you as applicant should be in a strong position by planet, aspect and house, and ideally the two rulers should be applying to an easy aspect (i.e. the 9th ruler and the ascendent ruler).
Consider also the 7th (contracts) and mercury (interviews, correspondence, general learning).
In your time frame you can't avoid the mars/uranus approaching conjunction, but you can either weaken it by hiding it in a succedent or cadent house, or working them to be significators (the classic lemonade from lemons).
Play around with the charts until the majority of the important significators are strengthened and the weak points weakened or intercepted.
No chart will be completely perfect, so just work to getting the most in positive light.
Check an ephemeris to get the general aspects down. For example, check out moon aspects when the sun will sextile Jupiter, or for example when mercury is in positive aspect with the mars/uranus conjunction.
And turn the chart wheel to rotate the planets in the most favourable positions.
Post your new chart(s) when they are ready, it might take some time, but patience will get you there.