MongoDB: Database too big to resync?
Yes, you are correct in both cases! Actually, it would be best to do both! 

First, increase the opLog size (at least 4x, 10x if you have space) and after that use backup method to copy all data to that node (lvm snapshot is best). 

During that time what copy takes, your new opLog (what is this time much bigger) will collect all changes and still keep that starting point.