The mentor system was extremely valuable for me in my prior internships, but as I transition into industry I feel that the impetus is on me to learn how to work without a mentor, which I think is what I'm struggling with.
It's a large, attainable project but on an unrealistic timescale.
Planes exist. This is a trivially-solvable problem. Yes, they cost money - but the time savings from improved communication will amortize that cost very rapidly.
If what they're paying you won't cover a plane ticket in a week or less but they're expecting you to ship features solo, GTFO. There's a clear line between "internship that pays below market because learning" and "bullshit job that pays below market because interns don't know any better".
On a final note, the whole "I need to learn how to work without a mentor" thing is really odd. That style of learning, IMO, actually becomes more important post-graduation...
There are plenty of non-intern employees who have mentors, that's how we do it at where I am currently working at least. I see nothing wrong with that, there's no reason why you wouldn't have one either.