Sorry it turned out that way, but I don't know what you could have done differently. You are gambling a bit buying one of these hubs. All of them are gummed up. If your indexing tabs are gone, that is indeed the problem. The indexing springs do fail, and to be fair were probably the most common part failure in the hub way back when.
However, back in the day, like now, it was much more common to just be a problem with old crappy grease than a failed spring. As you can see the spring is delicate and the spring pressures at play are quite small. Any gummy old crud in there will cause it to malfunction.
I mean I guess you probably could have bought one that was advertised to be "working", but I imagine that costs more and then you still would have had to tear it down anyway to clean it out before you could have any expectation it might be reliable.
As you saw in that video, you can test indexing in your hand to verify it works before you put it together. It's not a "bad hub" because the spring is bad. Yes you should chase down a spring. I know it is Inconvenient and expensive.
As for the other low speed spring you mentioned, or the high speed spring for that matter, those just work like the retarder spring on any other coaster brake. They are tabbed into something solid and drag on something that turns. Only a small drag is needed. You should be able to figure out how to look for broken tabs and and test those out of the hub too if you are worried about it.
Best of luck going forward.