Well, I tried so many things, hoping that some of the next TextKit API would finally provide a way to precalculate the needed height for a UITextView with a given width and text. Oh well.

UITextView+WhatFuckingSize

// HOW THE FUCK TALL DOES MY TEXT VIEW NEED TO BE?!?

@interface UITextView (WhatFuckingSize)
+ (CGSize)sizeThatFuckingFits:(CGSize)size withAttributedText:(NSAttributedString *)attributedText textContainerInsets:(UIEdgeInsets)textContainerInsets;
@end

static UITextView *FuckingTextView;

@implementation UITextView (WhatFuckingSize)

+ (CGSize)sizeThatFuckingFits:(CGSize)size withAttributedText:(NSAttributedString *)attributedText textContainerInsets:(UIEdgeInsets)textContainerInsets
{
    UITextView *textView        = [self FuckingTextView];
    textView.attributedText     = attributedText;
    textView.textContainerInset = textContainerInsets;
    return [textView sizeThatFits:size];
}

+ (UITextView *)FuckingTextView
{
    if (FuckingTextView == nil) FuckingTextView = [UITextView new];
    return FuckingTextView;
}

@end