We ran into something similar with the school librarian when DS8 was in K . I started by sending in a note saying DS had my permission to check out books in such-and-such series, which DS was wanting to read, and were well above K grade level. Later, I met with her to discuss DS's interest and aptitude in reading. I asked for her help to ensure that the content in books DS wanted seemed appropriate for a 6 year old, but that DS could be allowed to check out books at any difficulty level he liked. She ended up becoming a pretty good partner for us at the school library.
I've had great success with both DS6 and DS8 with reading above-level books. DS8 just recently finished the Lord of the Rings series (by his own choice), which at the beginning he said he was "struggling" through. I'm sure he'll be re-reading it soon, now that he's muddled through it. He admits that it's much easier and clearer now. The same thing happened with Harry Potter, which he started when he was 6. Beginning with the 4th book, he found it more difficult to understand, but he struggled through it with limited understanding and then a month or so later, re-started the entire series. (He has now mostly memorized the series after having read it a dozen or more times.)
DS6 is not as avid a reader as DS8, but he REALLY wants to keep up with big brother. He spent his entire K year reading the first 3 Harry Potter books. And he's proud of it. I actually asked him to take a HP break for a while to have him read some other good stuff for a few months, but he's reading the 4th book now and pleased as punch to be doing it. It's too hard for him now, but gets easier every day.
I agree with you -- especially with these kids, if you can find things that they WANT to do that are hard, you've just GOT to let them.
Good luck!