The Archdiocese has finally realized what a treasure it has there, and has put up a page on its website and is actually selling copies.
There are links to the "north tapestry gallery" and the "south tapestry gallery" where you can view all the panels.
Most of the "art" in the building is appalling - the usual 'modern', 'meaningful' stuff which means that it's (1) nonrepresentational (which is stupid in the context of religious art) and (2) deliberately ugly, as so much modern art is. So many artists have been trained in this style, and it is very difficult to get them to look at things in any different way. I think the two worst items in the whole place are the Tabernacle (which looks like three lengths of crushed, corroded leftover copper pipe from the salvage yard) and the ugly, androgynous, distorted image of the Blessed Virgin.
Where Nava, the tapestry artist, went right was by using photography as a base. Then at least his saints look like human beings.
I'm a Protestant so obviously I cannot share the full appreciation you will have for the stories behind the martyrs on these tapestries. I noticed, however, that the tapestries include one of the Korean martyrs from the days of intense persecution against Christians, Andrew Kim Taegon. Since these tapestries are from a cathedral in Los Angeles, it certainly makes sense that a Korean martyr would be included on that tapestry.
Andrew Kim Taegon was the first Korean to be ordained as a Roman Catholic priest. He died as a martyr in one of the early persecutions which tried but failed to stamp out the Korean church. The cathedral of the Archbishop of Seoul is today built on the hill where a group of highly educated Christians from the Korean nobility met in secret as a house church, were arrested, and were eventually persecuted and (in most cases) killed for refusal to reject Christ.
You may be interested in this book about the martyrdom of early Korean Christians, who in the earliest days were all Roman Catholics:
http://books.google.com/books?id=QMUCAAAAQAAJ&pg=PA34#v=onepage&q&f=false
Korean Christianity today is largely Protestant. That was not the case initially; the first converts learned about Christianity either from the Chinese or the Japanese, and the Korean church was initially led by laymen of noble ancestry with no ordained clergy. When missionaries arrived, they were shocked to find literally thousands of Koreans worshiping as Christians without priests, without sacraments, using lay catechists as leaders, and generally receiving baptism only at the time of death from the hands of laymen since no priests were available.
You'll note in the account of the martyrs of the early Koreans, with very few exceptions their testimonies are generically Christian and not specifically Roman Catholic. They were killed for their allegiance to Christ and not for specific Roman Catholic observances, and as a Protestant, I don't have a problem with respecting their sacrifices and willingness to die rather than renounce Christ.
Interestingly, the author of this book — writing in the mid-1840s during the rise of liberalism — points out that during the days when Europeans were rejecting the church and harassing Roman Catholics in Italy itself, people in far-away lands were suffering martyrdom under tortures quite comparable to those inflicted by the Roman Empire a more than a millennium and a half earlier. It seems pretty clear that things have not improved since the 1840s; Europe is becoming increasingly hostile to the gospel while much of the rest of the world is far more fertile soil for the truth.
