Just FYI Home isn't abandoned. On The Physicist (the_physicist) AO3, it's actually complete. 41 chapters of Spirk-y goodness.
The fic we're talking about called "Home" is actually different from the one you mentioned, but since you pointed this out, I'll just take this opportunity to rec both fics :)
The one we were talking about is:
Home by Lanaea
A mishap brings the Enterprise back to Earth for a while
Warning- extreme case of wip, it hasn't been updated in like 4 years
The one you're talking about is:
Home by The Physicist
Jim is heading towards a personal crisis. Their mission is vitally important: to find a new home world for the Vulcan race in the face of alien opposition. Soon it is clear that there is only one planet that will do. To secure the mysterious planet Jim must play his hand perfectly, but guilt at not having been able to save Vulcan and the responsibilities of captaining the Enterprise are wearing him down. Determined to be professional, he forces loneliness upon himself until a kiss he shares with his first officer changes everything.