From your sources we can deduce two things:
1. It was proposed by a Northerner for the purpose of winning over Southern states.
2. It had Southern support.
So the south ended up not having full representation in Washington because they insisted slaves were property and not citizens.
You said as much. The North did insist slaves were property and not persons, and for this reason, thought they should not be counted.
Let's go back to the source you provided:
The three-fifths figure was the outgrowth of a debate that had taken place within the Continental Congress in 1783.
To receive a full answer then, we must know what this debate was. Your source points us to the right direction, though not explicitly. It is referring to the proposed Article XI to the Articles of Confederation that read:
all charges of war and all other expenses that shall be incurred for the common defnese, or general welfare, and allowed by the United States assembled shall be defrayed out of a common treasury, which shall be supplied by the several colonies in proportion to the number of general inhabitants of every age, sex and quality, except Indians not paying taxes
It was a Southerner from Maryland, Samuel Chase, which proposed that this draft be altered to read "white inhabitants." He said black men were property, and thus should not be counted when distributing tax burden, much like horses or oxen were not counted as 'inhabitants either.' It was John Adams, a northerner, who said that tax burden should apply to all people, regardless of status, not just freedmen, because laborers produced taxable wealth, whether free or not. The southern argument followed that slaves were only a tool used in the production of wealth, not actual producers, and should not be counted.
http://www.cooperativeindividualism.org ... ation.html (Don't dare argue this is a "liberal" source.)
This is in 1783, four years before the later compromise. The southerners would win this argument through James Madison, who proposed that a 5-to-3 ratio be used instead (from your source). Read Article XI of the Articles of Confederation. A 5-to-3 ratio of slaves would be used to determine tax burden, but still be property.
In 1787, it was a question of representation in Congress. Northerners argued that slaves, being property, should not be represented in a Congress that would only represent free men. Southerners rejected this - slaves were people now, though they were not four years ago, and should be counted fully. This issue would be settled by Wilson, who would apply Madison's 3/5 rule, to the population issue. Wilson employed a southern solution in his proposal. The North was using the argument made by Southerners only four years previous when trying to distribute tax burden - that slaves were properties, not people, and should not be counted.
It was not the North depriving the South.