Re your plan:
1. I'm dubious this is a top-priority. I'd probably focus on the content for a while before focusing on swag and other perks. Patrons, especially early patrons, are there to be supportive. They aren't looking for "things". They want more of your quality stuff in the world. (This is just my attitude as a patron. I could be wrong. Are your patrons are clamoring for stuff? Have you asked them?)
2. Why not focus on the content and going viral organically? You're already at the top of HN. Keep doing more things like this and save your money! Have you seen First Round Capital's holiday videos? They get tens of thousands of views. I don't see any reason why your videos couldn't organically get a similar number.
3. If you have a newer phone, the cameras are pretty solid and probably good enough for a first video. I've used a DSLR in the past to make a medium-quality music video. I'd even consider using whatever webcam your computer comes with and doing something super low-budget to start, such as you simply saying the lyrics. Another quick improvement idea: instead of a static screen why not put the lyrics in the video?