Hi all - and thanks Marko and everyone for all your responses. I am one the owners of the two cats in question.
I should point out that we taken Marko's suggestion and have absolutely no intention of brining a dog into the house until we feel reasonably sure our cat problems have been resolved. I think we both fell prey to wishful thinking when we saw those cute "little" Rott x Burmese Sheep dog puppies at the shelter, but - being generally level-headed people - cooler heads have prevailed.
Now, about this cat problem: this is a situation we've been trying to live with and address for the better part of a year an a half.
So here 's a rundown of the situation (sorry, it might be a little long, but there's quite a history):
My girlfriend and I each brought a cat into our relationship (both cats are and have always been indoor cats):
"her" cat is Bubbles, 9 yrs old female, (spayed). This cat has never lived with other pets and was adopted as a kitten from a pet store. She's always been a little agressive and quick to scratch.
...and "mine" is Dezzie, 5 yrs old female (spayed). I adopted her from friends who were roomates in a large loft. Dezzie lived with several people and 5 cats. She got along well with the people and cats.
When my girlfriend and I moved in together, we moved into a new place (new to us and to both cats). Dezzie, however, suffered a traumatizing move. During the move into our new place, we had some renovations done. The workers were at our house during the day for a little over a week, and would often work with the windows open. One day, we came home and couldn't find Dezzie. We searched and assumed that escape through the window. After a week of searching, we found no sign of her. However, a few days after the renovations were finished, we heard her under the floor!!
We tore open the floor boards and she crawled her way out, all grey with dust - she was likely under there for the better part of a week at least. Brought her right to the vet (of course) who rehydrated her and gave us some special food to get her back on track. She got better in no time and even seemed relatively unscarred by her experience: after the first day or two, she came out of her hiding spot and was back to her old self (jumping up on my lap while I read my Shakespeare, eating well, etc.).
Initially, we made sure that both cats were separated. Dezzie was in our office (where I spend most of my time) and Bubbles in the living room (where my girlfriend spends much of her time). The door to the office is a french door with windows so the cats can see each other through the door.
While they were separated, we did quite a few of the things people have mentioned (swapping scents, feeding the cats on either sides of the door in sight of one another, letting the cats explore each other's spaces, swapping their scratching posts). We did this for a month while Dezzie recouperated.
When we finally got the vet's green light to let the cats meet briefly "in person," a fight immediately broke out: Dezzie ran away (and peed all over the floor), Bubbles ran after her, claws and teeth bared. We had to break up the fight before anyone got hurt.
We went back to the begining, keeping the cats isolated, and we continued to do all of the things mentioned above for a while. After a week or so, we tried to set up short "meetings" with a cat carrier. That was no better. Dezzie wouldn't even approach the carrier, Bubbles would not stop clawing and biting.
We kept resetting the process and trying again, until one day when Bubbles had Dezzie cornered and we couldn't break the fight up fast enough: Bubbles lost a tiny bit of ear to Dezzie who was just trying to get away from her.
As a result, Dezzie spends most of her time in the office (much of it with me, at least) and when she gets the chance to roam around she generally refuses to explore. Bubbles - however - roams through most of the rest of the place and is all to happy to mark her territory when left in the study. We even tried vet-prescribed "downers" for Bubbles but it had no real impact (save a stoned cat) and getting her to swallow the pills twice a day was a nightmare!
The major issue is that Bubbles is relentless: as soon as she catches Dezzie's scent, she will run at her and keep running at her. And unlike most cat fights which involve some hissing and batting with paws with both cats eventually retiring to their respective corners, Bubbles is playing for keeps. (I've been hurt pretty bad by Bubbles while trying to break up one of the worse fight, which doesn't help our situation either.)
We just learned about the Feliway thanks to all of you, and even after 2-3 days, we can see a marked change in the behaviour of both cats: Bubbles seems a little less aggressive and nervous; Dezzie seems a little braver. Of course, we're not yet ready to call this solved, but this is probably the first real sign of any type of improvement in the situation.
SO. The million dollar question: what now? What's our next step with these little gals? How long should we wait before trying to introduce them again?
Can't thank you all enough for your suggestions.