"Normally you would put thin wallboard up over something like this. I
suppose you could popcorn directly on the plywood and paint it but I'm
not sure how well that would hide the seams.
Why bother wtih the wall board? You still would have to tape the edges.
(But, as mentioned below, the wall board would give your some fire
Get the thinnest 2" wide "lath" you can find and use it to cover the edges.
You might consider a few extra pieces to create 4'x4' square on the ceiling.
Depending upon the look you want, you can paint everything white or make the
lath strips a darker tone.
If you like the "wood look" you can stain & varnish or just varnish.
The main problem, in my mind, also existed in the original installation:
you have a very flamable ceiling. Any fire starting in the basement would
involve the first floor very quickly.
That's why you might want to tear out the wood and replace it with drywall.