I say no. If the experience is critical to your interest in and candidacy for medicine, include it in the personal statement. If not, we (readers) can find out about it in the experiences section. I have a relatively consistent way of reviewing applications before the interview and would not be inclined to go read the other essay as directed in a personal statement.
I applaud your commitment to staying on topic and being concise. It is very hard to write concisely, and I am always impressed with applicants who are strong writers. This is a change of perspective I had after I used to be disappointed in applicants who are weaker writers, which over time I came to realize are the majority.