I’ve had success with Jasco Premium paint remover from Loews. As I recall, I let it sit for an hour or so and wiped off. It took maybe 3 coats for each piece. As mentioned, the wood is a very thin veneer so try to stay away from scrapping the old varnish off and sand very lightly. Here’s a pic of a refinished piece, a stripped piece and original.

Good luck & let us know how it turns out.