What are my options to terminate my lease early due to unemployment?

I'm sorry to hear of your employment situation but unfortunately it does not entitle you to terminate your lease early.

However, you are on the right track in terms of how to handle this situation.  A face-to-face meeting will be best.  Under the circumstances you are liable for the remaining rental payments until the end of your lease term.  However, the landlord is under a duty to "mitigate damages";  this means that they must use reasonable efforts to find a new tenant.  If they do, then at such time, you are relieved of any further rental obligation.

Perhaps, you know of someone who would like to move-in?  This certainly would solve your dilemma.  Ask around, see if any family, friends, former co-workers, etc. might be acceptable replacement tenants.  Also, ask if you can sub-let the unit; in effect you then would  become the "landlord".  Under the circumstances, you could charge the sub-tenant less than what you are paying but at least it would give you some monetary relief.  Something is better than nothing.  Again, you would most likely need your landlord's permission to do this.  But it's a possible option for you here.