I wanted to go ahead and update this thread as I have had the exact same issue this year and the same dilemma and I THINK I have a confirmed answer from a Disney rep who seemed very confident in the answer… (I’ve had some who totally did NOT get what I was even asking!)
We also have a 7 day park hopper and party tickets for one day in the middle of our trip for MNNSHP. If however, you have the regular tickets and the party hopper tickets on the same account it WILL let you make the FP reservations for the party, but you are limited to only 7 days (they don’t have to be consecutive) within a 30 day time frame by the system. So essentially, you will be blocked from making reservations with your regular ticket for day 8 as you have used your 7 day limit up. The rep I spoke with this evening confirmed that he has this question from foreign travelers a lot as they are also limited to 7 days even with the purchase of a 10 or 14 day park hopper.
I was previously told IF you buy the tickets for the party on a separate MDE account apparently you can get FPs from 4-7 that day (theoretically from what others have said, but I haven’t tested this to be sure).