I had a similar situation. I told my boss "I'm moving to X in the a few months, do I need to find a new job or can I work remotely?" Luckily I was able to keep my current job even though there isn't a large culture of remote working at my company.

Your odds of success, both in getting your request approved and in succeeding remotely highly depend on if there are other remote workers in your company and on your team. I'm the only one working remotely on my team and sometimes things are unnecessarily painful or inefficient because I'm the "special snowflake" that's not present at the office.

Don't mention the pay cut unless they negotiate that with you. You shouldn't be 25% less efficient working remotely, and you'll save them money by not having to allocate office space, electricity, etc, to you.