My chain is getting a little on the slack side, the EBBs adjustment is as tight as it will go. Should I just bang one link out and carry on riding, or should I get concerned about chain wear and start changing sprockets and chains?

I tend to use the chain checker on singlespeed same as I would on a conventional geared bike and change chains when they get worn.

If I have problems with a new chain not meshing then I look at the rear cog and front chain ring and change if necessary, although sometimes reversing the rear cog is enough.

Personally I run it til the chain is pretty much shagged then flip the ring/cog around and fit a new chain.
It’s a SS it’s supposed to be less fettling. Unless you’re buying ti rings/cogs replacing your chain all the time will prob cost more than a new drivechain.

What he said tbh – its a SS not a Blinglespeed