Perhaps the issue is that the ling is too sandboxy & free-form?
If you give them an IC purpose (succ the HoP!) that they have to work towards, it may limit the ammount of succed bystanders "just because they can".
They can succ people to work their way towards the target, but the goal becomes the target, not the succing.
Also creates an incentive to be discreet, adding to the rounds paranoia.
Also, IMHO all ling rounds should be solo ling. It will help the antag craft a cohesive conflict, as opposed to the current whackamole.
A completely different idea for ling:
Instead of killing the succed taking them out of the round, add them as the lings imaginary friend.
1. The ling now absorbs the memory of the succed (converse with the imaginary friends).
2. The victims are not taken out of the round, and are given a unique way to interact and roleplay with the antagonist.