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Your easiest route, I suspect, would be to have someone who *does* have Frame to convert it to MIF for you. Further, if they happen to have Mif2Go, they can also easily convert it to .rtf files that shouldn't require an xtension.
I feel rather sorry for you that you must work in Quark for tech pubs, but that's another issue entirely!
If the originator of the files isn't able to help, contact me offlist and perhaps I can help. I have Frame 6 +HTML at home, and Mif2Go as well.