If I want an ENS name that is in the expiry grace period, what's the best way to maximize my chances of getting it once the grace period is over (assuming there would be other contenders)?

icebreaker.xyz/0xen |
https://gallery.so/Oxen/galleries | https://opensea.io/collection/farcats

Assuming others are going to be willing to pay the premium (which looks like it's $2000 for a basic name) - is this just as simple as writing a script to do this and hope I am fastest or are there other tricker things I should consider (for example, trying to guard against front running)?

webmaster @ bob loblaw's law blog,  ʕ•ᴥ•ʔ

I don't think front running comes into play since this is a two step transaction, but are there other tactics similar to that which would disadvantage me?

Front running shouldn't come into play. 

If it's in premium just don't tell anyone you're looking at it, and be sure to price it appropriately and set a reminder. 

Check out this dashboard for historical premium purchases: https://dune.com/makoto/ENS-premium-registrations https://i.imgur.com/wPxztKI.png