Marcus Millichap releases an amazing data report every year on different markets across the country on different data points such as job growth.

Should I release them from the current lease and draw up a new one or should I just add an addendum holding them to the terms of the current apartment and just state that they are moving upstairs?

It just involves some sacrifice leaving home for extended periods.

Just because it's been listed for an extended period does not take away from the value.

Is the lender willing to extend the sale date further out? 

Extending Dennis' point, anything which requires a license (practicing law, being a real estate agent) remains the same.

I've done the lease extension technique as well, except I never offer a reduction in current rent to extend.

Redfin just released their future business model today, albeit only in BOSTON right now.

I've certainly heard of lenders extending LOCs to successful investors who have a strong relationship with the bank.What do the full numbers look like for this as a rental?

If it says they are responsible for the entire lease or until released then that is what you can do.