Ok, I stripped out all permissions from the Members group except the Fake permission set I defined. I also removed the Manage Lists setting , so it seems like they should have basic Contribute permisssions at this point, please correct if I'm wrong. Afterword, I tried to enter an item through the form, but the information still fails to get submitted properly to the list. The debug output below shows the return result after it tries to commit, of course when I get redirected to the Calendar view I defined for the list, the item is not there.
All permissions removed except custom Fake permission set
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Custom Fake Permission Set
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Chrome Debugger output
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Might not be obvious from the pic , the error reported in the return is 0x80070005
All permissions removed except custom Fake permission set
Image may be NSFW.
Clik here to view.

Custom Fake Permission Set
Image may be NSFW.
Clik here to view.

Chrome Debugger output
Image may be NSFW.
Clik here to view.

Might not be obvious from the pic , the error reported in the return is 0x80070005