>>2681478Perhaps consider the 150-600mm F5-6,3 DG OS HSM Sports. Maybe one of the better options if you strongly want to stay under $2000.
Otherwise, get the Sigma 120-300 f/2.8. It's a pretty decent budget alternative to the Nikon 300 f/2.8.
With lenses like this, you can also consider if you perhaps simply could rent one when you need it.