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The only thing that may change the outcome is a letter of intent. This means committing to the school it it accepts you. Letter of interest will have no impact.

Letter of intent allows the school to boost yield. LOI means nothing unless you won a Pulitzer or were named valedictorian since the deferral
 
Everything you have suggested will just annoy the admission staff. Do not do this.
And the school knows that you're interested in them, because you sent them an application.
I feel like you tend to apply the rules at your schools rather universally, when that's not necessarily the case. This is outright untrue for 2 schools (Mayo, and WashU) just off the top of my head. I think perhaps Jefferson too. idk about the policy at OP's school, but I feel like there's a lot more nuance to such discussions (whether on this topic, or the importance of thank you notes, etc.) than you sometimes make it seem.

Personally, I would recommend OP to ask on that's school's specific thread, or discuss with their contacts that were accepted to that school.
 
I feel like you tend to apply the rules at your schools rather universally, when that's not necessarily the case. This is outright untrue for 2 schools (Mayo, and WashU) just off the top of my head. I think perhaps Jefferson too. idk about the policy at OP's school, but I feel like there's a lot more nuance to such discussions (whether on this topic, or the importance of thank you notes, etc.) than you sometimes make it seem.

Personally, I would recommend OP to ask on that's school's specific thread, or discuss with their contacts that were accepted to that school.
OK, you named two schools, which are among the Top of the Top.

There are another ~138 to go in the MD world, and we have a fair sampling of Adcom members (some of whom are at T-Stratosphere), and I am only telling you what the collective wisdom says.

In the absence of a poster mentioning U Penn or Mayo, I'll go with the most likely response that an LOI will generate.