For minion damage, I think it needs to be compared to other monsters, not PC hit points.
So level 1, 4 damage and level 11, 8 damage?
Player HP triples by then. How about level 1, 3 damage and level 11, 9 damage?
Looking at what a level 11 skirmisher can do, say grimblock ambusher, their minimum is 6 damage, average is 11.5 damage. 8-10 damage for a minion seems reasonable to me.
An Angel of Battle, level 15 skirmisher, does 6 minimum damage, and 10.5 average damage. Again for a minion, 8-10 damage looks good.
You don't suddenly want your minions doing 15-16 damage at level 15, when that's about the maximum damage for a skirmisher of that level.
At level 21, wildhunt hound does 18 max damage, and your minions are dishing out 20. One wonders who to fear more, the 4 minions on the right flank, or the 1 skirmisher on the left flank?
your damage threshold makes minions much more difficult to kill, especially at low levels. Beware low levels!
The damage threshold is only for one-shotting the tough minion. Otherwise, they get bloodied with one hit, and die on the second hit. Doesn't matter how much damage you do, so against that 15 threshold minion, you could do 4 points of damage from cleave bloodying it, and 5 points from a breath weapon, and the minion would be dead. Or your walock could curse it and eldritch blast it for 16 points, killing it in one shot.
I also wouldn't use the threshold/bloodied mechanic on every minion, just the ones I wanted to make tough.