And the odds of playing that key card on T3/4 are just as high as the opponent who opened 5/2 and got it then.

This is wrong because Expedition causes a shuffle. You will play your $5 later on average if you get it using Expedition.

Later on average, yes, but the same chance of T3/4 as someone who opens 5/-. On T2 you draw all but 3 of your cards; in the 90% of cases where you then get your $5, your T3 hand is EC[C|E], plus two of the eight cards in your discard, which includes your $5 buy. So you have a 25% chance of playing it T3, and a 62.5% chance of playing it T4, with a 12.5% chance of missing the shuffle.

The person who opened 5/- has a 44.4% chance of playing it on both T3 and T4, with 11.1% chance of missing the shuffle.

The person who opened 3/4 without expedition, however, has a 0% chance of playing the $5 on T3/4.