3D Printing Faceup on FDM?

Typically, people who print in PLA does so to get a rough model that they then refine using fillers and primers (and lots and lots of sanding) and eventually cast in resin.
It's nearly impossible to get a bare filament print smooth enough to use the face up techniques usually used on BJD.

Would painting the head in a more traditional manner be an option?

 

It's not impossible at all, but it takes a lot of work, priming and sanding to get a PLA print smooth enough for a faceup. I've done it 3 times so far, since I don't have a resin printer nor the skills to do a cast. However, I don't think it's safer than just going ahead with a resin printer.

You need a primer (I personally use Mr Surfacer 1000 and 1500), paint for the skin color (either brush-on or spray paint), and lots of sanding between the layers, which take at least an hour to dry respectively.
Also, the downside of this is that if you want to redo the faceup, you're going to wipe the paint and possibly some primer as well, and you'll have to prime, sand and paint the skin color again before you can give the head a new faceup.

But as far as your question goes, it is possible to get a PLA print smooth enough for a traditional faceup.
Here are two of my heads for example:

Spoiler

 

I think you've made the right decision, hahah, I can't wait to finally own a resin printer myself and leave all this priming and sanding behind.
I do use a dremel for smaller nooks and crannies like the ears and eyeholes, but most of the sanding is done by hand. And to be honest, I'm not a very patient person either, as you can see on the ear of the first head. Sometimes I just don't care enough to get everything super smooth, as long as it's for personal use and the face itself is smooth enough for a faceup, hahah.