I don’t know this specific work - I’ve done lots of other minimalist music, though.
Marking your ‘countdowns’ is a really good idea.
Does this one have a lot of metre changes? Marking a two with an ‘L’, a three with a ‘△’ (a triangle, in case that doesn’t come through) and a four with a ‘▢’ (a square) does two things - it gives you an easy visual reference that reinforces the time signature and the act of marking it/writing it yourself helps you to pay attention to it.
In your home practice, toss a grapefruit or similar sized object from hand to hand, so that you always catch it on the downbeat. This helps to give you a kinetic sense as well as an intellectual sense of the timing.
That’s the trick with Steve Reich - the repetition forces a type of listening that’s much more intense than anything one is used to.