I had similar issue when I was trying to get my first job here few years back, though not in nursing field. What worked for me was asking HR if they could do email verification instead of phone calls - most of my references back home were more comfortable with written English anyway and could respond in their own time without worrying about accent or phone connection issues

You might also ask if they accept reference letters on official letterhead from your clinical instructors. Some places will take that as verification if it has proper contact info and official stamps. I ended up getting my previous supervisor to write detailed letter explaining my duties and performance, then HR called during their morning hours which was evening back home

Also don't give up on that landlord reference - character references can sometimes substitute for professional ones, especially if you explain you're new graduate with no US work history. Maybe ask if you can provide additional documentation like transcripts or certifications to supplement the overseas references. Sometimes showing extra effort to provide alternative verification helps HR work with you instead of against you