While not directly answering the question, I would strongly recommend you use a DB management application. phpMyAdmin IMO is a nightmare to work with, and as you have discovered, very difficult to manage large files.
If you are on a Mac Sequal Pro is a really amazing app. If you don’t have external access to MySQL it supports SSH tunnelling so you can SSH to the DB server / a server with access to MySQL. You will be able to import / export pretty much any size DB with that.
If you are on windows, I have used a couple of different programs, I would recommend HeidiSQL. It can also do SSH tunnelling (little more effort required).
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