I scheduled mine for the same time that I am having my 2nd fitting. It is the only time the full picture will be put together before the big day.
I did mine about 3 months months before the wedding. My work schedule wouldn’t allow me to do it the same day as final fit. If you can, I agree with pp, try to do it the same day as 2nd or final fitting.
Never even thought of scheduling the second fitting and HMUT on the same day - love that idea! It's all about the same timeline, so it makes sense to book them around the same time, if not on the same day.