It would be common enough for rings to get stuck with a long interval between running. Was there any difficulty in getting the motor to turn over smoothly without a "hitch" due to rust on cylinders? Rust can wind up breaking rings. At this point you've already run it so turning it over by hand may not tell you much. I would set the car in a place where the smoke will be least objectionable and let it run. It will either clear up--or not At that point you can take a compression test to help decide your next move.
My best result with a very frozen motor (rust in the cylinders) was with a Triumph GT6. The motor wouldn't budge with the crankshaft front pulley bolt so I removed the starter and used the flywheel ring gear to pry it a little bit back and forth after putting oil in the cylinders. It took a day of this till I had it turning over OK and re-installed the starter. When it fired up it blew an unbelievable stream of burnt oil out the tailpipe (sorry Earth) and it took a full 3 hours before it cleared up. So - there is hope. Good luck with your B16 - Dave