If I've understood your requirement correctly this is relatively easy to achieve but needs some specific inputs and custom formatting, see attached
I've set up a custom date format to display just the month in MMM style and applied this to columns D and E and the range AB7:AM7. I've also set up data validation on columns D and E to named range "year" on Sheet1 range $A$54:$A$65 which contains the first day of each month from July to June. The user simply picks the 1st day of the start month in column D and the 1st day of the end month in column E. The 1st day of each month is entered in the range AB7:AM7. The FTE for each month between the start and end dates is then given by the following formula
in each cell in the range AB8:AM40.
I've also added some simple code to set up a new year on the Set New Year button.
Regards
Ian
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