This has been the recommendation when traveling to the US since 2001, only that the worry was NSA rather than ICE.
The procedure that I got recommended in 2005 was to install a second fresh operative system (preferable windows) on the laptop on a separate partition/disk, make a copy of the old boot partition and disk encryption headers, encrypt the copy and store it online for later retrieval, and then overwrite the old boot with the new installation. Make sure to leave the old partitions alone.
The restore is then as simple as downloading the encrypted backup, decrypt and dd it back in place. Repeat the process before taking the trip back. It was advisable to test the processes before to familiarize yourself to it, and to use the fresh installation a bit so it wasn't completely blank.
The procedure that I got recommended in 2005 was to install a second fresh operative system (preferable windows) on the laptop on a separate partition/disk, make a copy of the old boot partition and disk encryption headers, encrypt the copy and store it online for later retrieval, and then overwrite the old boot with the new installation. Make sure to leave the old partitions alone.
The restore is then as simple as downloading the encrypted backup, decrypt and dd it back in place. Repeat the process before taking the trip back. It was advisable to test the processes before to familiarize yourself to it, and to use the fresh installation a bit so it wasn't completely blank.