I would not. I have stripped and refinished pieces of furniture. It's a messy process. I can not imagine doing it to an entire ceiling

Horrible task. if you get part way through and decide its too much work, you cant stop. Washing a ceiling is bad enough.

Would. Not. Do. It. Under any circumstances.

I helped apply it to a ceiling at a weekend house my mother had built years ago. High peaked ceiling over family and kitchen area and we were higher than kites ourselves when finished. Bad air circulation in room's peak, bad fumes. While my tongue looked normal, it was several hours before it felt like it fit correctly in my mouth ;0)

Are you sure it's varnish and not shellac? if it's shellac you can remove most of it easily with denatured alcohol. Just make sure the area is well ventilated.

If it's just the color that bothers you you could put a gel type of glaze on top and tone it down....or rub thinned white paint into it for a "pickled" effect.

Whatever it will be a big uncomfortable job and you will have new appreciation for Michaelangelo's Ceiling.

You'd have to be on a scaffold lying on your back just like Michaelangelo all right.

Do the varnishes now have new formulations that prevent yellowing? Otherwise you're going to end up with the same look in a few years.