Most modchips should play the backed up imports just fine. As mentioned above the DMS3 chip would be an excellent choice. I absolutely love mine.
Here are a list of it's features:
1) Direct boot of PS2 originals/imports/backups (all media, including DVD-9 and multi-disc titles).
2) Direct boot of PSX originals/imports/backups (anti-mod and multi-disc titles supported).
3) Macrovision disable.
4) DVD region free.
5) PSX import screen position fix.
6) Boot any PS2 executable directly from memory card. (DivX, Mp3, Logo etc.)
7) Loader code contained in flash and upgradeable via software by the PS2 to support future feature enhancements. 2 copies of loader code stored in flash. Copy 1 is not upgradeable. On bootup, the hardware will determine whether copy 2 is valid and if not, fallback to copy 1 (protects against reflashing failures).
8) All console versions supported.
*Note that last one isn't entirely correct. If you have a Version 9 or higher you will have to get the DMS3 chip that is designed for it. There are 2 different DMS3 chips. 1 that works with V1-8 consoles and the V9 chip (which I believe also works with the newest Version 10 but don't quote me on that).