Did a bit of editing to forestall commentary on origin.
What is the total size of the videos now? If you have to compress them, you will inevitably lose some quality in this process. If it is done well, you may not notice it on playback.
Do you want a blu ray video, or are you just trying to back them up as data on a blu ray disc?
MultiAVCHD will be able to take multiple input files and build a new blu ray video for you. But if the videos you have now are not already compliant to blu ray specifications, they will be re-encoded to fit those requirements. And anime does better with a particular encoding profile in X264, that MultiAVCHD may not utilize.
So, examine the files with MediaInfo and see if they need to be re-encoded or not.
The other issue is the fact that MultiAVCHD is a picky beast, prone to crashing. But it is the only free program that will build your blu ray video with a menu so you can select each episode. There are commercial programs you could try instead.