I believe the fault is with After Effects trying to handle 32 bit full float EXR images.
Try this, Save your EXR as Half Float (16 bits/Channel), then in After Effects (with the regular color space, not sRGB), interpret the EXR footage as usual with the Straight - Unmatted alpha, but the key is tick on Preserve RGB in the Color Management tab. It’s trying to apply linear light to the EXR sequence which appears to be muddying up the color for no apparent reason.
Hope that works.
Edit: I thought that worked, something went wrong though, still looking into it!
Edit2: I’ve tried almost all possible combinations, and unfortunately all I can say is After Effects just won’t reproduce the same picture you’ll see in your max render buffer. You can get close, but you’ll probably have to adjust curves/levels to get the same-ish image. Perhaps now’s a good time to learn Nuke or Fusion :surprised
Edit3: If you ignore the alpha, however, you get the proper colors. Your final alternative could be rendering the alpha out separate and importing it; could work.