You're probably better off using a 3rd party tool to convert the disk to GPT like http://sourceforge.net/projects/gptfdisk/ (in order to pull it off without data loss). The challenge, and part you didn't mention, is if this LVM is also the boot partition, or if this is a secondary, data-only partition (which, if it isn't, it really should be).
Otherwise, a program like richcopy ( http://technet.microsoft.com/en-us/magazine/2009.04.utilityspotlight.aspx ) or robocopy ( http://www.microsoft.com/en-us/download/details.aspx?id=17657 ) will help you do things the way you've requested, by migrating data and shares.
Always make sure you have a good backup before doing either of these operations.
There is also a nice GUI for robocopy you can get from a technet article. We use it for all our large file share transfers.
http://technet.microsoft.com/en-us/magazine/2009.04.utilityspotlight.aspx
The easy way is to take out all the storage media in your PC and install only your new SSD and an optical drive if you are using that for the clean OS install instead of the preferred USB drive.
Install your OS, drivers and run Windows Update and install all your regular applications.
Install your HDDs. Ideally, you would want to move all the data you want to keep off your old boot drive to the new HDD then wipe the old HDD (delete the partition and then create a new one & format it). You can then move back any files you'd rather have on that drive. This is the best way to get rid of your old OS and any associated files that are now orphaned.
Use Microsoft's RichCopy tool to help your file moving efforts. It's way better than File Explorer and more efficient.
It is not perfect and not supported by Microsoft but it does do a great job nearly all the time. Here is the link to a TechNet article with a download link. The Wikipedia article briefly mentions some of its issues.
MS Richcopy will allow you to skip bad files. It also has a log, so you can see which files were skipped.
Maybe after the initial copy, you can go back and decompress whatever didn't copy.
http://technet.microsoft.com/en-us/magazine/2009.04.utilityspotlight.aspx
In my personal experience it is going to be far less headache to just do a downtime copy. DFS for just moving files is complete overkill. Especially since you don't have any experience with DFS.
Robocopy for this task is perfect. You can have it copy all the files and folders for you, and it will tell you what files it was unable to copy. So then you won't have to play missing file search for your users over the next few months.
Also there is this awesome gui for Robocopy if you don't want to have to use the CLI syntax.
http://technet.microsoft.com/en-us/magazine/2009.04.utilityspotlight.aspx
I hope you only have your games on the 1 TB as the things you want to uninstall. If this is the case, you do NOT need to uninstall your games even if you do a clean install of your Windows on your SSD.
You have 2 options with regards to changing from Win7 to Win 8:
A) Run the "Upgrade" option where Windows 8 will overwrite your current Win7 installation and retain all of your customizations and program installations. You also retain any legacy drivers, files and registry settings from all the things you have done on your PC since installing Win7. You will also have a giant hidden area about the size of your current Win 7 OS that has to be manually deleted to regain the drive space.
B) Do a clean install (wipe your SSD and install Win as if you were installing a brand new SSD with OS). You will lose all your customizations (unless you use the EasyTrasfer feature) and will definitely need to reinstall all applications. The big advantage is you clean up the registry and the Windows folder so there will be no legacy Win7 files at all or any leftover junk from old applications and whatever elese you've done just by running Windows 7 for a period of time.
Games don't usually need to be redownloaded (especially ones from Steam). I believe Origin still needs the game install files (which are kept with the Origin client by default not the actual game files that you play from), so if you set up Origin right, you'll be golden there too.
Finally, 500 GB just isn't enough space to back up a 240 GB SSD + a 1 TB HDD unless you have a boatload of free space. The best you can hope for is to select to backup only the most essential files with a limit somewhere close to about 200 GB per backup.
If you need to move a bunch of files around, Microsoft's RichCopy tool is awesome. It's been around nearly forever and still works better than any drag and drop file manager.
If you want it done faster you can download Microsoft's ancient (but still quite effective) free RichCopy tool. It works great even on 64 bit Win8. Here's an article about it.
What are you using to copy the files over? Robocopy xxcopy? Explorer? Rsync? Something else?
My guess is that if the drive isn't a problem (and you've already stated that it was ok right up until you started doing the copy) then the problem is far more likely to be either an issue with the network or something "interesting" about your files. I know I've seen very bad performance using windows explorer to copy files across the network if there were lots of small files (< 100Mb) - copying larger files got much better performance.
You might try looking at either RichCopy http://technet.microsoft.com/en-us/magazine/2009.04.utilityspotlight.aspx or the Microsoft File Server Migration toolkit to see if you get better results from those. http://technet.microsoft.com/en-us/library/jj863566.aspx
You should get the USB adapter regardless. That is a handy tool to have. Just get a universal one, then you can connect pretty much anything by USB (laptop or desktop hard drive, CD drive, even a floppy disk drive)
If they didn't delete the windows partition or format it, then bringing it up as an external drive on another Windows system should work. Everything should be accessible, although you may need to take ownership of the directories you need access to.
I like to use Rich Copy or Roadkil's Unstoppable Copier for this kind of thing because it retains the file metadata (modified date, etc) but can drop the security information so you don't have issues with it on the machine your copying to.
If these guys did format or delete the partition then you'll need a data recovery tool. Bootmed, like most other Linux based rescue CDs, uses TestDisk and PhotoRec for data recovery. Bootmed is designed for users who aren't familiar with Linux, so it's supposed to be a bit easier to work with, which is the only reason I recommend it. Ubuntu, GParted, etc all have these tools too.
EDIT: The thing with Bootmed or some other Live CD is you can use it right now with the drive in place. These all have File Explorers too, so if there's a readable NTFS partition, you'll be able to see your files and copy them to an external drive (even though it's not Windows). As long as you can download a live CD image (ISO) and burn it to a CD (as a disc image - please ask if you don't know what this means), you can work on it as soon as the CD is burned. No waiting to get an adapter.