I agree with ColdCase. Using the 3TB drive connected to your TC via USB is probably the best solution.
I swapped out my TC drive long ago (had a 500GB first gen too), but I used a new drive to do so.
I noticed when I took the old drive and mounted it, it was formatted HFS+, but it also had three partitions in total, with two small partitions being hidden from view when accessing the TC on the network.
The TC created those partitions again when I formatted the new disk, so I assume they're required for the TC to be able to use the drive. I was able to swap the old and new drives in the TC without issue afterwards.
I'm not entirely sure that if you use an HDD that's already HFS+ and stick it in the TC whether it will create those two partitions without destroying the data already on the disk (or whether it needs those partitions at all), but if they're your only copy of your music library I wouldn't risk it.
You should look into backing up your data on another drive, then you'd be able to install and erase the 3TB HDD and copy the contents back onto the drive. You can even remove the HDD temporarily after it's been formatted by the TC and copy the music using a dock (for faster transfer rates) then reinstall it in the TC.