How is approach #2 easier? Isn't brushing on liquid sandpaper easier than
sanding mechanically?

Light sanding takes very little time, and you may even escape cancer. Just
read the warnings on Liq. Sandpaper. It's serious stuff.

What did you use as the varnish (or the protective
top finish)?

We used satin finish semigloss acrylic interior paint.

I see. Basically, you tried to preserve the existing varnish as much as
possible.

The poly varnish on ours was in good shape, and it made no sense to remove
it, as it is an excellent base for paint, once primed.


, I might as well go with a strong chemical stripper
like Jasco (which claims to remove 6 coats of paint/stain), then I don't
have to deal with sanding.

Jasco is another highly volatile chemical soup that is very bad for you.
Just read the label and weep. I use it only for small jobs where prior paint
is way too thick, and hides all detail.

Prime is unlikely to hide grain if the doors were poorly sanded in the first
place. Undercoat is a possibility, after priming. It tends to even out the
surface a small amount.