Return day number, knowing day of week, weeknum, month and year

Hi all, and HNY!

Another new-year hours-tracker request I'm afraid...

Right, I've got a workbook in which the following is listed:

The year
The day of the week (in format "Monday, Tuesday", etc.)
The week number (1-52)
The month (in format "January, February", etc.)

I've got a cell for each day of the week. I'd like to auto-populate this with the number of the day in each month, i.e. 1 for the 1st of each month, etc, not 1-365.

I've had a go and just can't get my head around it.

Sheet is attached. The cells I want to populate are highlighted in orange.

Mega-thanks in advance, and I hope 2019's good to everyone!