I wouldn't restrict myself to anything in particular. Especially at your price range, there are many products that are great in integrateds, AND separates.
You'll get more bang for the buck on an integrated as a general rule, but that's no reason to limit yourself to anything. When you get locked into one idea, you miss out on some great things. If I had been locked into the idea that separates rule, and they are the only thing for me. . . Then I would not have even auditioned the inegrated I have now, and I would have missed an amazing piece.
I'd have to agree with Hantra -- unless you have an absolute need to keep the FT around, keep an eye on for any solution. You mentioned budget of $500-600 and cost of additional interconnect. First, do you see yourself falling into the "hobby' or trap of continually upgrading down the road, or are you pretty much trying to stick to a specific budget for now and the future? Granted many of us have started that way, only to find years (or months) down the road that funding meant for the rest of your life has been redireted towards audio....
I've heard good things of the Monarchy, but figuring cost of FT + interconnects + Monarchy and you end up in the same territory as integrated such as the Audio Aero Prima, Unico, Mesa Tigris, MF, Creek, BV Audio, Plinius 8100, Arcam, etc.
If you think you're succeptable to audio-nervousa or upgraditis, stick the the integrated -- it will put some shackles around you, and if you want to try something new, stick with integrateds as well -- it will leave you with one singe thing to swap out.... The more devices the more variables...
On a budget, and unless you''re a give-me-every-detail-want-to-hear-the-exact-recording-even-if-its-awful person, you might want to towards some of the hybrid integrateds.. Keeps you at your price point, still able to properly drive the Quad's, and gives you something a little different or special in presentation vs. a lot of the budget amplifiers whose character doesn't seem THAT different... If you are more of that, look towards maybe a BVAudio integrated....or heck, while you're figuring things out, give one of the cheapy digital receivers a try.

I have and have had everything from 3w and 5w 2a3's and 300b's to PP's to digital amplifiers to SS amplifiers to way too many integrated to vintage receivers to passive preamplifiers, TVC passives, active preamplifiers, and everything in between... Some of the cheap stuff, combined with the right speakers was great, integrated or not -- some of the ultra expensive seperates I could say the same thing about, but for which was a horrible match with certain speakers..
One thing that I've done a lot, in addition to seeking out other owners of your speakers and learning about their experiences is to contact plenty of dealers that sell them, far away dealers and make it clear that you wouldn't be buying from them, and get advice on what they've liked, whether they still sell them or not... In addition to the peanut gallery's comments (me), no harm in chasing after people who have been through the same thought process you're going through already...