Question: Can the connection within a ten be stronger than the common connection at the convention?

Answer: These are completely different things. Connection in the ten is your personal connection with your root.

However, connection with all the people attending the convention is the connection in width, not in height. Therefore both are necessary.

Question: How can we convey the correct intention to the center of the ten in order to achieve a connection of the branch with the root?

Answer: I believe that if we follow the articles of Rabash and Baal HaSulam, we will ultimately reveal the entire network of connections between us and the Creator. Then, it will become clear that we already exist within this.
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From the Daily Kabbalah Lesson 9/15/24, “Continuing the Congress With an Ascent”

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To the Convention with the Force of the Ten
Convention: Absorbing Others
The Whole Convention Is One Group Of Ten