Why not make a wake-up mechanic? Like giving your teammates a "slap" to wake them up. I think it'd work great cause it would be a both rewarding and risky mechanic. Rewarding, cause you can wake up your teammates from Haze's (and eventually new hero Rem) sleep, obviously, and risky cause you need to go into melee range to wake up your teammate, which is already bad enough (easier for nukers like pocket or lash to hit both of you), plus heroes like haze could use this mechanic for their advantage (dash into sleeped enemy and pressing parry, to bait their teammate).
I think this would generally make the game more interesting, plus I know how much everyone hates Haze's sleep.
I think this would generally make the game more interesting, plus I know how much everyone hates Haze's sleep.