One other thing...

The nice thing about pro video cams is they often come with remotes so you can start the video while sitting at you keyboard.

Over 6 years ago I did a short video of my brother on a grand playing the prelude for his daughter's wedding.

I used my XH A1 plus a Rode boom mike. I like the sound. I did no EQ just posted it as is. In today's world, I would EQ with more midrange and bass to reproduce the sound as it was live.

https://vimeo.com/8440065