How to access Time Machine files from previous OS install?

Hey all!

I've dug around the boards for a couple of days and have inched closer and closer to a solution but I'm stuck now. Hopefulkly someone here has some secret sauce they can share.

The Gear:

- Macbook Pro (late 2011), let's call her Chloe

- Time Capsule 1TB

The Old Setup:

- Chloe was running mountain lion

- Had (have) 8+ months of Time Machine backups

- Chloe was exhibiting very high running temperatures, took it in to be fixed

- She went in for repair to have logicboard replaced

- Technician gave me a Macbook Pro as a loaner machine (I put my HD in there for the couple weeks while my system was in repair)

- During this time I did a clean install of Mavericks on the Chloe HD (previous Mountain Lion install was exhibiting oddities, running generally slow and beachballing like crazy for months, so I wanted to do a clean install).

- Did not use migration assistant (didn't want to risk bringing over whatever was causing the problems), happy to reinstall apps from scratch and/or move everything over manually as needed

Outcome:

All good.

The New Setup:

- Chloe and Chloe HD are back home, running nice and cool temperature wise but...

Enter Time Machine:

That brings us to the present and a couple of questions...

- Is it possible to access my old Time Machine backups? (Right now I have to hold Option on the Time Machine, go to "Browse Other Backup Disks" and I can view the old Time Machine backups but ... even though the Time Machine dates on the right had side go way back, they are pink and unaccessible.

- If it is possible to access my old Time Machine backups, can I "rejoin" this backup and continue TIme Machine where I left off? It's 900GB worth of data that goes back for months, I'd hate to have to reformat the drive to make room for new Time Machine backups of this new "Mavericks" Chloe install.

Thanks in advance if anyone can help!