Just because an item is up for sale doesn't mean it's worth that much. A Champions Lance +3 is worth maybe 20 million maximum. Anyone stupid enough to pay more than that deserves to lose as much gil as the buyer can get.
Bloody Lance Head +3 is not in the game, it's not an item that can drop. Not all mobs drop +3 versions of items. Weapon heads are one of them. Iron Plate +3s don't drop either. How SE will change Champions Lance synth to accommodate this remains to be seen.
HQs will become common. If I could guarantee a crab bow HQ by having all HQ mats I'd have made dozens of them by now. While I have indeed made dozens anyway the majority were +1s. The new HQs will be equal to +2s and +3s.