I would not try another cooler.
What I WOULD do, is figure out if it is hitting on something OR if you are using the correct hardware selection from the kit. Installation of the U14S, which I've done probably fifty times or more, shouldn't be difficult at all. You do need to start each of the four screws by only a few threads, and then work around in a criss cross pattern until snug.
If you can't get it to work then it is possible. and LIKELY, that you have either used the wrong mounting hardware or backplate, or are using the wrong standoffs. Probably the wrong standoffs. Keep in mind that hardware comes in that kit for MANY different platforms and you MUST use the correct ones for the platform you are using. In this case, you need to use the correct backplate and standoffs for the LGA 115x platform, which includes LGA 1150 and LGA 1151, both Intel.. If you try to use the AMD standoffs or other hardware, you will run into exactly the kind of problems that you are seeing.
This explains YOUR specific installation, for any cooler using the SecurFirm 2 mounting system, which is what you have with the NH-U14S.
View: https://www.youtube.com/watch?v=G0mDubVwZuw