Is there a common best practice for what I am trying to do?
No, there are no best practices for what you are trying to do. Your categorical variables, time series, and numeric variables don't have to be the same size. Therefore, there is no need to vectorize your single numeric input, nor should you. You just need to have that variable as its own input. If it is only one number, then so be it.
On a related note, fusing multiple data types is an exciting emerging area. This review article will give you ideas on how you can perform integration: "Fusion of medical imaging and electronic health records using deep learning: a systematic review and implementation guidelines".