Wood creaking sound (intermittent, but persistent), how to finally put it to rest
You say it's not your ducts, but I just listened to your video and I've heard that sound before, it's the sound of expanding metal uptight against wood and slipping.  The fact that there's a similar noise coming directly from the vents at times just means that it's coming from hangers that are having trouble holding onto your duct work, some of which has padding between in and the ducts preventing the resonating tinny sound, where as in other places it's not dampened and thus you hear it along the duct.

It's clearly not a critter so it's better off just left alone.

Loosing some hangers may actually be the solution.

Similarly, changing how fast your hvac system heats up / cools can help you troubleshoot. Open all the registers in your house and take note of how often you hear your noise. Now on a day with similar temperature and humidity try the same test with only one register open.  If lower airflow means less noise then reducing your your blower fan speed should help and vice versa. 

Other fixes to try if it's still bothering you:

If the sound is relatively new (you've lived in the house before and this is the first season where it's been a problem) you can try to tighten down or loosen all screws and hangers related to the duct.

If the sound has been there for almost as long as you've had the house, you can try adding rubber or plastic spacers to your hangers and anywhere else the duct-work might be in contact with the wood. 

However, my guess is that your particular noise is buried inside an inaccessible part of your house, else you probably would of pinpointed the cause of the problem. Thus the next most reliable solution aside from ripping out and replacing all the duct work with properly insulated circular ducting, or a different kind of HVAC system is to add an acoustic duct liner.

If it were my house

If I was experiencing the same sounds those ducts also carry AC, i'd just wrap the exposed duct-work with neoprene insulation to prevent sweating and reverberation of the sounds and the next time I change the flooring add an acoustic padding.

Similarly, I might try reducing with the blower fan speed depending on how accessible that is.

If you are rich and can afford to pay for quiet:

If I were rich, I'd just remove the entire central air system and replace it with a ductless mini-split heat pump system. Not only will this eliminate the noise, but you'll have:


Better zone control.
A large space in your basement freed up where your furnace and control system currently is.
No unsightly ducts running though your basement and taking up
space in your walls if you ever choose to finish off your basement.