The Reds' transit route, including timings for each leg/ sector are published in NOTAMs, so anyone with enough airmanship to read them should know when they are due through any given area of airspace and look out/ avoid accordingly.
As long as aircraft are squawking then hopefully the Reds will pick them up on TCAS before anything untoward happens.
WRT birdstrikes. 2000ft is plenty of height to deal with a birdstrike! Especially considering all military pilots are trained to deal with birdstrikes tooling around at 500/ 250ft!