I deal with a company that has a unit in a larger building. They have a
few servers in a room that normally sits in the low 70's during the day.
The problem is however that the main building is now shutting off the
AC at night and on weekends. This causes the server room to spike into
the 90's.

There's no access to water or drains anywhere nearby. There's no access
to outside walls, and they can't punch through any even if there was
because they just lease the unit.

Most spot coolers like the APC Network air's require a drain line for
water. I was thinking perhaps since they have a netshelter rack of
suggesting one of the ARU doors to just suck out the hot air and vent it
into the ceiling, but those are about $2200.

Anyone have a similar situation with a solution?