In the first place your need to understand what you have there. A tough and reliable old motor, state of the art when it was new. Having said that, you must understand that was then and now is now. Back then, those motors were expected to be very inefficient, smoke, and make a mess. That's just the way it was. So don't be alarmed by the smoke and drainage. What you can do is make sure it is operating properly, and adjusted properly. Getting the thermostat working was part of that process. Then use it and enjoy it.
Hmmmmm, I'm wondering, are you running it on a boat on the lake, or are you running it in the yard on muffs or tub? If you are, well there is half your problem. It was designed to run on a boat on the lake.
If I am not mistaken, that one has a automotive-type distributor, right? As simple and reliable as any car of the day. But fouled plugs were common also, especially if not running and adjusted properly. Back to the basics, get it out on the lake (yes, with your new thermostat), and run the daylights out of it to burn off the accumulated oil and crud caused by running too cold. When done, you probably will find it smokes less, and is cleaner.
To answer your question, yes the strong spring goes over the vernatherm valve.
EDIT: Sorry, I had not yet watched your video when I wrote all that. At least my suspicions were correct, you are running it in a container---a pretty nice one, I might add. I'm not so sure that is all smoke. Sure looks like a lot of steam mixed in. Steam is normal, how much is too much, hard to say. The thermostat does force it to come up to 140 degrees before it opens, then it mixes with hot exhaust gasses. What is the outside air temp? Cold and wintery? You might want to actually check the powerhead temperatures.