I looked at the picture and it looks like a psychological test

Without some background of what I am looking at it is meaningless. How about the AVS forum link discussing this?
Looked up your zip at the Mits consumer site - Oh My God - you have 19 service centers within 20 miles. Surely one or more of those can get it right. Shipping on the face makes no sense and could crack the mirror. It can be done but we would not take that risk (if we had to move one). Upright is how it is shipped from the factory to retail.
In home service will vary and should not be expected. An ASC is only obligated to either repair it in home or provide the labor and transportation for pick up and delivery. The reason for this varies from the philosophical to the practical. I do On-Site service but if I were in New York that would not be practical at all. As noted you have plenty of choice - see who will do it your way.
The price seems steep on the surface but I have not torn into one yet. Some products are straight forward and others require near complete disassembly. 1st and 2nd gen Mits is straight forward. We charge less than what you were quoted but prices vary with location due to the local economies. you have choice so I would call around, explain that you have a problem that will need a tech to look at it and one company already said it needs a cleaning and you would like to know how much they charge for that if their tech determines the same.
BTW, taking that Mits list and comparing it to the NESDA service centers for your area could be VERY helpful in finding quality.
http://www.nesda.com/locator/state_search.php
At this point I am going with the cleaning until you give me more info about this blooming video. Tech wise, that is a CRT term that relates to the way that beast works. An FPD can't bloom! They can clip either burying blacks or turning variations of peak white into one solid form. Solarization is another FPD performance term...