The overheal effect doesn't disappear, you set the damage cap to the amount you want the player overhealed, such as -175 for demo.
If you don't want demo to be able to use lots of stickies to do the jumps easily, set the damage of the trigger_hurt to -350 (or higher, as high as you like really), the damage cap to -175 and set 'no physics force from damage' or something like that (it's the last option) to yes. This will also stop soldiers from dying except on big syncs, so you would need to add in another trigger_hurt for those.