How do I restore files from TM backups with broken links?

I have Time Machine backups with broken links all over the more recent backups.

I get the message "The alias “xxx” can’t be opened because the original item can’t be found." whenever I click on one of the links.

I have made the backups on my external usb backup drive before before upgrading my internal disk to a larger one.

Two questions: 1) How can I recover the files? 2) What happened, how can I repair the backup if possible?

The sequence of events was: Made the latest backup. Apple ran extended diagnostics overnight at the store and did a reinstall of the OS (10.8.2). I passed on restoring the backup and went to an authorized service center and had them put in a new tera-byte drive. I deleted (in the star-wars display) the oldest two and a middle backup leaving the Aug, Oct, and latest Nov. backups.

Now I see 100's 1000's of bad links. If I look at the backup (just look) with finder I can see directories for July and Sept in addition to the ones I didn't delete.

It appears that the files are probably all there and I could recover them a few at a time if I poke around.

I am tempted to do this before trying to repair the disk. Yes, it will take me ages; but I would rather take the time than a chance at doing -Anything- that could even possibly make things worst. I can see 3 senarios and wonder if anyone can say what would be best. And by best I mean **Safest**.

1) Go in TM to the Aug backup that seems to have no (or maybe only a few) broken links and restore that; then move in TM to newer backups and restore one folder or file at a time on top of it.

2) Do the same thing with a restore of Aug but then use the finder to copy newer files from the backup disk to the new disk.

3) Do essentially the same thing; but do it all in finder.

Of course that still begs the question of what happened and if the backup can be repaired; but to me, that is secondary to getting the data back.

fyi- I have looked at the TM hints and debug-repair file. I realize I can try a repair disk but I am tempted to try to get the data 1st unless someone is Sure a repair won't mung the data more.

Thanks