I apologize many times over for the length of this post!
I am looking for advise on a series of problems with our collection storage
that are interrelated.  First, a little background to explain the structure.
The Museum is a 1936 replica of a stone house which stood in Nacogdoches,
Texas from circa 1790 until 1902.  The desire in 1936 to replicate a
stone house that the town felt remorseful for having demolished has led to
no end of trouble trying to fulfill their other goal of starting a museum.
(I don't know which goal was on first.) The Museum's collection storage is a second floor
room built in 1991 as a "lean-to" addition to the 1936 stone structure
designed to look like a lean-to added to the original house somewhere
around 1850. The downstairs area is an office space.  The collection space
is generally 15 by 40 ft.  Access to storage is limited to one oak door at
top of wooden stairs that also lead into the upstairs gallery of the stone
house.  The space has its own HVAC unit but no humidistat at the moment.
The RH was consistently 55% for three years, then dramatically rose to 70
one year.  I have dehumidifiers cranking non-stop to keep it below 65 now.
(The humidity in the the stone structure has never changed from 55.)
We have isolated some of the causes, but not all.  The back of the HVAC
closet return air space, which backs up to the stone wall of the 1936
structure, is not closed.  In other words, we can see stone.  The upper
portion of the closet has a sheetrock wall, but the return air portion
was left unfinished.  We found insulation stuffed into the area which had
become saturated and had fallen down.  The addition has a continuous roofline
from the stone structure.  But apparently, the stud wall connected to the stone
structure has no exterior, so that behind the sheetrock in the collection room
is stone.  The exterior of the addition is board and batten with the walls
connecting to the stone building shaped to fit the stone but the ends are
unsealed.  The HVAC unit is too large for the space, I'm told, so it rarely
runs.  Will a humdistat solve this problem?  Does the open space
between the addition and the stone house
mean moisture can migrate not only through the gaping hole in the HVAC
closet, but also through the sheetrock wall?  Is there some sort of sealant
or other process to mitigate the problem?  A review by the fire marshall
suggested a second access to the storage by adding a window large enough to
remove collection pieces if the stairs are no longer accessible.  Another
suggestion was a steel door and frame to further isolate the collection room
from the remainder of the building.  At the moment the collection room has
strong security and I'm relunctant to install a window in the space.  The
window can be shuttered, as most of ours are already, and I can add other
security measures to tie into the existing security system.  I need to balance
security, fire prevention and response, and humidity control.  I have money
right now to implement the window door and repair to the HVAC closet.  I don't
know what to do, if anything, about the flow of air between the addition and
the stone structure.

I thank you in advance for your patience in reading this far, and for your
advice.