The thing is, as far as I'm concerned, the band never recorded any footage inside of the studio during the making of HT. The basically started producing Making-Of documentaries with Meteora because they wanted to show their creative process, and as Mike hinted in Get Me Gone, disprove that they were a studio-manufactured act. You can see in the beginning of Making of Meteora Phoenix is talking about how Mike came up with the idea for the album, which to me implies it was really the first time they thought about doing it.
Obviously there might be some promotional photos of the band inside the studio but I doubt there's any footage, let alone enough footage to constitute a documentary.