Thank you @Francois for your answer.
Actually, projecting on the default anatomy, exporting and then importing to the intra-subject seem like it could work. It just brings a little issue. Some of my data is getting old. Back then, the default anatomy was ICBM152 and now it's Colin27, making the whole deal incompatible.
Here's my new question: How can I make use of the same default anatomy across "studies"?
Thank you again!