Scrap the blue or pink foam idea. Its always a recipe for frustration. White bead foam never causes this problem but it is a bit more messy.
Have yourself an arrow puller, use the grip to rotate the arrow go clockwise so you don't loosen up the field point, then pull the arrow out.
I'm not sure it's a great idea to twist (rotate) a carbon shaft that's stuck. Arrow pullers don't do much in the cheap foam and lubricants can make the arrows plunge deeper. Once the arrow goes deeper and past the lubricated end, then it's really stuck.
Correct. Arrow pullers and lubes wont do a darn thing. Been there, done that. The friction created heat fuses/melts the blue and pick foam and binds it to the shaft. This foam works with slower trad bows but that's about it. Cut your losses and try 2" thick panels of the white bead foam. We make broadhead targets for sale locally (too large to ship freight) but we only Etha-foam and never have issues (even with the fasted bows) with friction/heat melt fusion.
I think At the range I shoot at they use strips of carpet stacked on top of each other... Works pretty well if you wanted a foam alternative. I don't think they are broad head friendly though