Here's another way to look at it. Don't run a macro but have a separate sheet with pre-built formulas to line everything up correctly. You could then save this as a template and just dump the data in each week.
Step 1 - create a reference page
Step 2 - name a range for the start date on the reference page
Step 3 - create an "output" sheet.
Step 4 - name a range (work.range) on your original data.
Look at the attached example - all this will make sense -
using vlookup for each name, test the "day" using the day function to see if the day matches the column header (12/13) for example, if it matches, the true value becomes the date and time from your original data, if it does not make, just enter nothing "". You're not 'moving; anything if over, but rather testing to see if the source data matches the criteria you setup.
Check out the example - good luck!
Rob