Here's a FormCalc script that will populate the months names beginning from the current one. Put it inot the exit event of the date field.
var oCells = Ref(Table.HeaderRow2.resolveNodes("#field[*]"))
var nDate = Date2Num($.formattedValue, "MM/DD/YYYY")
var nMonth = Num2Date(nDate, "M")
var nIndex
for i = 0 upto oCells.length - 1 do
nIndex = 12 - (12 - Mod((i + nMonth) -1, 12))
oCells.item(i) = Num2Date( Date2Num( Concat(nIndex + 1, "/1/1970"), "M/D/YYYY"), "MMM")
endfor
The result looks like this.

Make sure that display pattern for the red fields is changed into date{MMM}!