Edit: A lot of people say, that GWM needs a melee weapon attack, but they miss Jesses point: While GWM requires a melee attack with a heavy weapon, Sharpshooters only criteria is an attack with a ranged weapon (not a ranged weapon attack). Jesse bases his claim on the fact, that a crossbow is still a ranged weapon, even if used as an improvised weapon for melee combat. That’s why it deals 1d4(!)+20 damage. (It works with any ranged, heavy weapon btw., so Longbow qualifies too.) Of course Jesse is playing the devils advocate here and of course, no somewhat sane Walter will allow this in any campaign ever, as it’s obviously not the intention behind these feats. But you could read it that way and that’s Jesses (paperthin) point. Besides: he finds the image of a barbarian running around recklessly smashing a crossbow over everyone’s head to just be hilarious.
Was with you until your final point. Per the “Ability Modifiers” section of Attack Rolls in chapter 9, making a melee weapon attack uses Strength. The only exception to this is weapons that have finesse, which the crossbow does not. And despite this being an attack with a ranged weapon, you are using it as a melee weapon attack.
Ah, my mistake there- I thought that was another one with "attack with a melee weapon". It does make more sense that crossbow bashing would be strength based tho, surprising to see the rules as written following logic XD