The problem is not with PHP, it's your hosts setup (not that I blame them for setting a low exec time and low memory, as they are serving many customers!) however, you could possibly have asked your host to do it for you. They should have SSH access to the server, and a good host would have been happy to import using SSH.
Have you tried using FTP? It's whole purpose for existence is transferring files (hence File Transfer Protocol) and can handle even GBs of files with relative ease. Any host worth their salt has FTP access, and most GUI FTP programs (like FileZilla) are as easy as drag and drop once you've found the www or public_html or whatever folder. Then from there it should be much faster importing the DB.