You also may want to talk to a local rescue organization for information on
finding a pet-friendly apartment.  They might have a list, or a volunteer
might be a landlord, or know someone.  We were also in a similar predicament
when my brother-in-law, who's house we were renting, decided to cash in on
the real estate boom and sell the house.  That meant we had to move.  We
started looking around for apartments, and were running into the same
problem with our 3 cats (at the time, now it's 5).  We lucked into a condo
that my husband's co-worker was selling, and honestly, the mortgage payment
is less than we would pay in rent.  Maybe you could buy something small?  We
are also technically over the pet limit for our condos, but all they will do
is fine us.

I applaud you for considering your cats in this situation.  As a rescue
volunteer, we get so many cats that are just left behind when people move.
Also a round of applause for your stance on declawing. I don't know how
people can value objects more than the welfare of their pets.

We had this exact same problem a few months ago (house to apartment, 4 cats in
a 2 cat town).  I was really starting to panic, too.  I knew it would be harder
to find something, but, I swear, the way some people reacted, you'd think I
said I had four anacondas.  In fact, they may have preferred that.  

Do keep calling around.  Even places you never considered before.  In every
community, there has got to be a REALLY pet friendly complex.  I didn't know
this until I had made the 40th call and stumbled across ours.  This place is
like a zoo (in a good way), and I never would have known about it--even from
asking around.  

The key to our success was their desperation.  It was November, which is a
really low point for new rentals.  They went out of their way to get us in
here.  You don't have the season thing working for you (although I would advise
you to rent something before school is out), but there are other kinds of
desperation.  If it is an option, I would look for a place that is slightly
more expensive than the apartment is worth.  These tend to be less desirable
"investments" for the average apartment hunter, and hence, probably unoccupied.

Ours is kind of a midrange place.  Low rent landlords have been burned by so
much that they will rarely give you a chance (the exception being low end
complexes--which are scary).  High end places are paranoid about having their
fine carpets shredded (and whatever else they imagine a cat can do).

Explain your desperation to the leasing agent.  If they won't budge, talk to
the owner/ manager.  In the cases where they were willing to compromise for us
(only 3), a sympathetic (or agressive/desperate?) agent went to bat for us with
the manager.  But it's very hard to tell during the intiial conversation if the
rules are truly written in stone or if the agent just isn't very imaginative.

Do try the Humane Society, vets, rescue groups, etc.  If they have a list, it
will at least weed out the places that don't allow pets at all.  This was of no
help to us, though--99% of these places had the 2 pet rule.

Offer every concession you can think of: an extra large deposit, taking an
apartment with older carpeting...  Expect to pay a lot more for anyplace that's
willing to work with you.  Most will want a pretty hefty pet deposit plus
monthly pet rent.

Some less than rational things I considered in my desperation:  bribery, fake
references, mobile homes (this was remedied quickly when we took a drive though
the "parks".  The number of Confederate flags used as window dressings was far
too disturbing).

You very well may have to end up lying about the number of cats you have.  I
realize now that I could have done that, but at the time I feared being thrown
out on the street.  My cats are so skittish that no one could count them if
they wanted to.  If maintenance came in unannounced (which they would only do
in an emergency), they'd be lucky to find one cat.  Just make sure there are
plenty of really good hiding places, and any self-respecting cat will take care
of the rest himself.  If you have those perverse dog-like felines that love
strangers and don't have sense enough to hide, then this option is definitely
not for you.

Good luck--I really do feel your pain.