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Just thinking at loud here...
What if you start by defining constant velocity and showing what its
position and velocity graphs look like. Then define constant, non-zero,
positive acceleration and show what its position and velocity graphs look
like. At this point, you have invested maybe 3 class periods if you go
slow.
Then move on to forces, momentum, energy, circular motion, gravitation,
whatever you like, returning to kinematics as later, say before you teach
projectile motion but after you teach vectors.
This way, you would have the vocabulary of kinematics in place but not the
equations. You would get to say things like: when no unbalanced forces act
on an object, its velocity graph looks like this,or like this but never
like that.
It feels to me that you could teach a lot of physics before you needed any
further kinematics treatment.