You also can find an FC that has access to housing and than ask if you can have access to the garden function and than crossbreed there.

Granted we've been advocating for them to add something more to apartments in order to make them more functional for those who don't have access to a house (and they may still there were talks of doing things) but there are other avenues to get it done.

Also, while having a powered chocobo is all fine and good you don't truly need one powered past ten (it's nice but it's not needed for progress). It is however best if you put all the points in one skill tree to make sure your chocobo is a specialist in something (if you leave it just at ten).