The Great Compromise did not really involve the people who wanted a strong national government. Both of the sides in the Great Compromise wanted a strong national government. The Great Compromise was a compromise between the small states and the large states. The only way that we can say that it advanced the interests of the people who wanted a strong federal government is if we say that it made it more likely that the Constitution would be ratified by the states.
The Great Compromise was a compromise between the large states and the small states. The large states wanted both houses of Congress to be apportioned based on population. The small states thought that was unfair and wanted every state to have equal representation in Congress. The Great Compromise split the difference, apportioning the House of Representatives by population and giving each state equal representation in the Senate. This compromise had nothing to do with how strong the federal government would be.
However, the Great Compromise did do some good for the people who wanted a strong federal government. The compromise satisfied the big and the small states. This made it more likely that they would all vote for the Constitution. If the Constitution was ratified, a stronger national government would be created. Thus, the Great Compromise helped make sure that the Constitution would be ratified, thus ensuring that the US would have a stronger national government than it had under the Articles of Confederation.