Hi S.. My daughter went through major separation anxiety coupled with other types of anxiety from preschool through first grade. We found some of the techniques mentioned by other moms to be helpful: the kissing hand, notes and stickers, a special "mommy daughter" necklace plus counseling. I also put a picture of our family in her folder that she can look at if she misses us, and created her own personal list of emergency phone numbers. I hesitated with this last one for fear that it might generate anxiety, but in my daughter's case it empowered her and eased worries that she may not be able to get back to us if something went wrong. May or may not be the case for your son.
If you choose to remove swimming as an extra-curricular, I would be sure to keep physical activity in his routine - maybe scheduled playground time that includes you? Exercise, nutrition, and time outdoors are really effective ways to curb anxiety. Don't let the mommy guilt-mongers get you down! This is about transitions and change that can feel threatening and overwhelming to little ones. My daughter and I spend TONS of time together and yet her anxiety far outstripped your sons. I really like the suggestion of giving him your undivided attention for the first fifteen minutes that you are back together. It makes the evening go more smoothly for my littles and for me. Good luck! Hard as it may be in the moment, this will get better