It’s true, ProEXR for AE can’t store the adjustment layers, which of course could be any effect(s) AE has, so not really possible to store it in the EXR file.
What you should do is render the image layers as you’re doing, build the comp in Nuke, and then manually add nodes in Nuke where the adjustment layers are, trying to duplicate them. Depending on which filters you used, this could be hard or it could be easy. If this is going to be your workflow, maybe just use the adjustment layers as a rough preview and do the real tweaking in Nuke.
It’s not generally possible to “bake” adjustment layers in AE because an adjustment layer effects everything below it. If you had one adjustment layer in the middle, you could pre-comp to bake it with everything below and leave the other layers separate, but in your comp the top-most adjustment layer only has two other layers above it.
Brendan