Problems with conversion to MOV

The native format for my JVC GZ-HM400U hd camera is MTS 1920x1080. I'm told to convert that to mp4 (no problem)and then convert the mp4 to mov with quicktime pro (I have purchased both the mpg and pro plugins for quicktime.) Quicktime loads and plays the mp4 ok but when I try to export to mov (I tried all the hd sizes here) all I get is a white screen or white strobe effect screen when I try to play the resulting mov file. I downloaded the K lite codec pak. Now I get error 36 I/O error when I try to play the MOV file. I attempted the conversion with MPEG Streamclip which gave me "Error. Cannot prepare file." Any suggestions?

Why would you convert it twice? When I do my final conversion for P5, I go directly from MTS in my HF11 to .mov

Although, granted, I do convert to MP4 proxies if I'm doing any CG or color correction, but when I do the final render I use the original file, not the proxy.

If I try to import the MTS file directly into Quicktime Pro, I get the message: "Error -2048. Couldn't open the file xxxxx.mts because it is not a file that Quicktime understands."

If I try to load the mts into Mpeg Streamclip, I get the message "Open File Error: Unrecognized file type."

I'm curious to know what software you use to convert mts to mov.
While I am told that some editors offer direct conversion from mts to mov, many do not (including mine) because of copyright limitations

Ahh... I use Adobe After Effects. Didn't your camera come with software? My Canon HF11 came with software that converts .MTS files to either .MOV or .WMV (I never installed it, though).