I believe that the striker is in fact at it's seat of power at higher tier lockdown. A probable way to mitigate this is a scaling health debuff. Here's how it will work:
The health debuff will be applied to every piece of equipment that provides any health bonuses, so it should affect heart trinket users to some degree, but enough to make them in line with the other classes.
Let's do an example from t2 lockdown. If a striker has maxed out 3* equipment, as well as 2 3* heart trinkets, the total health would be 19. However, if there is a -2 debuff on each piece of equipment, including the trinkets, it should subtract a whopping 8 bars of health, giving them only 11 bars total. Now before you scowl at me, note that this idea applies only to equipment that has a health bonus, so people who don't have any trinkets on as we'll as people who have other types of trinkets will be mildly affected.
The health debuff will be as follows: -1 for t1, -2 for t2, and -3 for t3.
This should put strikers in line with everyone else.
the most practical is: increase and decrease the health in Lockdown based on "percentage", or maybe, mixed
ex.: (just to think)
Striker loses 50% of "total" health
Guardian earn +25% of "based" health and plus +4 health bars
Recon earn only 7 health bars
this will not prevent you to use the health trinkets, but will mitigate the effect of these in Striker example
in Guardian example... the "percentage bonus" don't will give additional health if wield the trinkets (just working on who use a high health set [if there is])