Check to make sure the water inlet valve for that toilet (at the wall) is fully open.

I just checked - it's fully open. I also tried to close it half-way, same problem.

An additional note - I tried to reset the pressure by shutting off the main water valve to the house and running the faucets. Once I turn off all the faucets and turn the main back on, the knocking disappears for about a week but then comes back.

Install a water hammer arrestor between the wall and the shutoff please.

I have had the same water hammer and the only way to make it stop was doing what you did, turn off water, open all the valves in the whole house (including flushing the toilets a couple of times), close everything up, turn on water. Fixes it every time but it returns. I had some arrestors like Joseph posted installed on my washing machine valves (easiest to get to), but it didn't help; I hope it does for you.

A water hammer arrestor will only help at the moment the water is shut off, correct? The knocking sound I'm hearing is while the water continues to run and fill the toilet tank.

I think part of my problem is when I had a bathroom remodel done (no water hammer before that) and the plumber was a bit of a bull in a china shop. I think some of his excessive pounding things into place caused a pipe (buried deep somewhere in a wall somewhere) to come loose from a strap holding it in place. So the noise I hear seems to be a banging, loose pipe somewhere. Could that be it?

We've also had this recently, ours stopped with the trick olychick mentions. But an emergency plumber on the phone said it could be the internal cistern in the toilet. Perhaps it's permanently running a tiny bit. They are quite easy to replace I think.