It's hard to say what would work for you without a template. You might be better served finding and posting a template you like, then seeing what can be done with it. If you're open to something macro enabled, take a look at the attachment - a template I've found popular with users. It isn't quarterly, exactly, but it does fit rather nicely on one screen. It uses a small VBA procedure:
...to track the selected date, and it updates the table to the right with the projects that are active on the date you've selected. It auto-updates with each click, and you can add more initiatives to your list and they'll be automatically included. The updating table to the right uses the formula below in AN3, array entered with Ctrl + Shift + Enter, then filled right and down:
=IFERROR(INDEX($AI$3:$AL$33,SMALL(IF(($AK$3:$AK$33<=selectedCell)*($AL$3:$AL$33>=selectedCell)=1,ROW($AI$3:$AI$33)),ROW(1:1))-2,COLUMN(A:A)),"")
This formula is designed to look at up to 30 entries in your initiatives list. If you need more, just change all of the "$33"s in the formula to something bigger.
People seem to like the interactivity of this template, and there are ways to doll it up with conditional formatting, additional info, etc. Take a look, or peruse Excel's templates to see if there's something you like. It's tough for us outsiders to know what kind of look would work for your business.
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