Did these suggestions work for you? If not, here is some more information regarding my experience with giving similar advice is with FCP 6 not 7, which does not require Snow Leopard Server in virtualization:
Firstly, to correct a misstatement above:
Rosetta is a default install in Snow Leopard Server; not optionaly as with Snow Leopard client.
Secondly, Final Cut Pro 6 and then presumably 7, was a Universal application that does not need Rosetta to run and according to roaringapps.com, it will run in Lion and Mt. Lion (and presumably Mavericks, as many report that Final Cut Pro 6 runs in Mavericks).
Final Cut Pro 6 installer has a "bug" that causes a Mac running Lion, Mt. Lion or Mavericks to report the "PowerPC" dialog box. There are two known solutions to this FCP6 problem that may work with FCP7:
1) Use Pacifist to install (http://www.charlessoft.com/) or
2) Use Jeremy Johnstone's Terminal method:
http://www.jeremyjohnstone.com/blog/2012-03-11-installing-final-cut-pro-studio-2 -0-on-mac-os-x-10-7-lion.html
A "partial application" migration might work, but only if you know where each and every element of the FCP7 install landed. Pacifist should help in this regard.