I'm not sure what calculator you're using, but If I had a 4' deep alcove to use as a trap, I would be pleased... I would line all the perimeter of the alcove with 4" of 705 (area of max pressure and min velocity) and frame out the opening. I would suggest looking at a Helmholtz Slat absorber, especially if the depth of the alcove is varied. You could create a great broadband bass trap with awesome extension.. look at using 1x5 wood slats and play with the 'slot' (space) width.. remember that the 'effective' thickness of the slat is 1.2x the thickness of the 1x wood (.75 x 1.2).. that's the way I do it.
Otherwise, you could create a broadband trap by hanging some 'baffles' of unfaced batt insulation inside the space and framing the opening then fitting approx 4" thickness of 703 into the front area. Cover the whole shebang with stretched fabric... You really can't go wrong.
Do worry so much about the 'peaks' in the response, as it is an absorber and it will definitely take the boom out of your room!!
Just do it!!