Not overstated in the slightest. By 1861 because of the 3/5ths clause the South had it's population inflated by around 1.8 million for the purpose of determining House seats. That was worth about 20 extra congressional seats to them.
Nonsense. The Free States still have roughly twice the number of Representatives as the Slave States (including those that didn't secede). Your claim is abjectly ridiculous. The South didn't fear being overwhelmed in the House, where they already were greatly outnumbered. They feared that the Senate would eventually go against them, since by 1860 (and for a great while before that) the numbers were more evenly divided. They believed (rightly or wrongly) that Northern preponderance in both Houses, in additional to the obvious electoral advantage in Presidential elections, would eventually be used against them to meddle in their internal affairs (extending beyond slavery) and to enforced economically disadvantageous trade policies upon them.