Would you trust hanging your camera which cost you $___ to hang from a DIY string? If the contraption failed, would you be willing to live with the consequences? Mounting a camera for video is more than just hanging it. You need to stabilize it and achieve your desired framing and composition. What good is mounting a camera if it twirls around on the string or sways with the slightest breeze, or drifts to filming the rug behind your back. Unintentionally shaky video can be dizzying to watch. Also think about the ease of accessing and mounting/dismounting the camera. How would you retrieve your video files, charge batteries, remount the camera in the same position if a take need re-taking. If you were a maker and used to building or inventing your own things then the situation may be a different story, however from what you have written it does not seem to be the case. Also consider the safety standpoint, you want to hang this thing over yourself to film the keyboard from above.
If you want the easy and lazy way of doing this, purchasing a tripod with a boom or side arm would be the best bet. Secure mounting and relatively worry free if setup correctly, this would be a wise way to go. The price may hurt initially, but after you've been recording for a few months you will forget about that and thank yourself for getting appropriate gear for the task. Also consider supports, mounts and tripods don't go obsolete quickly like the technology they hold, you don't need to buy a new one every few years if you choose appropriately in the first place.
If there happens to be a secure place to anchor a GorillaPod or similar, then you may wish to investigate that route. Not as pricey as a tripod.
There are a few instructables that turn up in searches for making camera mounts. Have you looked into them?
You could spend money trying to find ways to avoid getting a proper tripod or mount, and after all that end up buying the tripod because you became frustrated with equipment that was insufficient for your needs, or you could just go out and buy what you need. Now some people may want to do the former because they like the process of making things, experimenting, failing, then making those things better based on what they learned in the process.
There are many affordable tripods on the market now. I'm not saying you have to go buy a commercial product as it is possible to make a camera mount yourself, but from what you have written it might be the better choice for you.
With regards to syncing. You could go the DIY low budget way here. Film your hands doing a clap, then sync the motion and sound in post. You could DIY a clapper board with pieces of lumber and a hinge, maybe add a slate if you felt like going further.