Alright I'm back down to this Last Word Quest is all sorts of stupid. Was up to 80, now back down to 60 and the people playing are getting sweatier by the match
Is that part of the chaperone quest?
There's an easy way to do it. Just make sure you only have TLW equipped when you pick up heavy ammo, any other time just use a primary you are comfortable with.
Equip an LMG, grab heavy, equip TLW, kill people with the LMG. Job done. The kills don't need to be TLW kills.