Monthly Grid Populated using Start Month, End Month, and 3 other potential factors

Made a couple of changes, highlighted in orange.
1) Put dates in row 3, then applied the formatting 'mmm' to the cells
2) Inserted a helper column (A), which may be moved and/or hidden for aesthetic purposes, populated using: =SUM(D$8:D8)
Then populated row 8 using the array entered formula*:

Formula:

=$C4*INDEX($F5:$Q5,MATCH(MONTH(F7),MONTH($F3:$Q3),0))*INDEX($C9:$C12,MATCH(COUNT($E8:E8),$A9:$A12,1))

*Array entered formulas are confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER (BEFORE copying across). You will know the array is active when you see curly braces { } appear around your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer.
Let us know if you have any questions.