My advice on the cover letter is to just be honest about your situation. If you're only going consider remote, let us know that. If you prefer remote but would consider on-site as you say here, let us know that too! It's all going to come down to a discussion about whether we're the right fit for you and you're the right fit for us, so it benefits both sides to be as candid as possible (just my two cents).
If you're thinking about applying, it doesn't hurt to email me and just say that you applied from the HN post so I can keep my eye out for it!
So I'm emailing you now with a cover letter and another attachment of my resumé. Hope you don't mind!