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Swing, swing, swing
"What's a swing" is a good question. I don't know how big a factor "more muscles" is, though certainly different muscles are involved. Maybe more importantly, a swing can accelerate the striking hand over a longer distance than a thrust can, and so builds up more speed (at the expense of taking longer). The striking point on the weapon ends up moving at an even greater speed – the further from the hand the point is, the faster it is (though the entire system is slowed somewhat by the weapon mass and the distribution of that mass, especially when much of it is far from the hand, so the net result gets hard to compute...)
And then there's more... But stepping away from physical detail and jumping to game play, right, my suggestion would suggest twice the power for swings, equating to about 1.5 times the damage. Just keep in mind that I'm not saying that's a "right" number for any reason, just one that plays well (in that the swing's damage multiplier is high enough to make it often worthwhile, but not so high that the thrust is never a higher-damage option).
Per your suggestion, yes, that could be handled instead by thrust damage with a +1 or +2 bonus per die. Basic thrust damage itself, too, could be reworked as you say, as some basic (punching, I presume) damage with a number of immediate special effects, without necessarily a damage bonus over that basic damage.
All that said, I think GLAIVE's basic setup is how I would handle melee damage if creating a GURPS-like framework from scratch: Drop any thrust vs swing damage progression entirely. Have only a single, basic progression for ST-based damage, which handles unarmed strikes; then give any weapon a +X damage add for thrust and a separate +Y damage add for swing. That sensibly sets the thrust vs swing damage difference as dependent upon the weapon's characteristics.