You're right, there's nowhere for the letter to go right now. ERAS isn't open, and it would probably get lost in the meantime at your Student Affairs.
What I did was just let the attendings know I enjoyed the rotation, and asked if they'd be willing to write me a strong letter of rec later.
As for fourth year letters, I got much more one-on-one time with the attendings in my chosen specialty, which offset the brevity of the rotation. However, the other difficulty with letters from fourth year electives is that you want most of your letters in when submitting your application (which starts Sept 15th). That only gives you July and August to find new letter writers.
Good luck.