I've always found that if I love something, it works! I think you're on the right track with clean, modern frames. Maybe add a couple of pillows or other accessories to tie the colors in with the rest of the room (you're starting from a neutral base, so it'll be easy!), and voila!

I would put them in a box frame that is completely out of plexi glass or what you call lucite. With a background of your choice but minimalistic probably cream or white, beige or dark brow. You sometimes see that in museums. And you can have it custom made for your size.

I think a good way to incorporate it, would be to frame it as you originally planned. But then add in one or two pops of color (that are found in the quilt) to your room. You can do this by adding one or two colorful pillows and perhaps a colorful vase / flowers.

You can still stay with the minimal, modern style for the pillows / vase. It's the color that counts. This might just make the quilt look a part of the room. At least it's worth a try.

Otherwise you could pick a favorite design blog and use their mood board services (it will cost you a few hundred dollars though) to help you incorporate the quilts into your design scheme. Good luck!

I agree-- If you love it, show it off! What about hanging it on the wall using a gallery hanging system (there's tons out there, but here's an example from Amazon: http://www.amazon.com/Gallery-Looped-Picture-Hanging-System/dp/B004CUR0JI)?

It'd be a sleek and simple way to show off the quilt and might modernize it a bit as well. Plus, if you ever get tired of it, you can just hang something else in it's place with the same installation.

The best way to create an interesting space is to mix styles shamelessly. Just put 'em up, and then deal with how they will make you want to mix it up in the rest of the space.

Drape one over the back of the couch to grab and snuggle with (if you're not using them purely for art). Or have one on the foot of the bed. hang one above the bed sort of like a mock headboard.

I'll bet the neutral, stark modern decor and the colorful, homey quilts will make each other more striking, rather than clash. And your space will be representative of more aspects of who you are -- which will make it more distinctive and original.

So I say: be bold, put them up.

As said before- If you love it, it will work. Treat them as modern art. Frame as you suggested, however I wouldn't add any other pops of color to tie them into a room. Art doesn't have to match your decor. Think of all the minimalist rooms you've seen that have one eye-catching work of art on the wall. That's how I think this will best work. Hang and enjoy.

Okay, the other comments are of the "be bold" variety, and I'm here to give you a couple less bold approaches just in case you need them -- if you love these quilts but feel they clash with everything else, take a good pic of them, blow it up, mute the colors or change to sepia or black and white, frame and put up. Keep the actual quilt folded on a chair or couch close to the pic.

Or -- get a small bed box/foot stool/bench at the end of your bed, fold the quilt into a narrow strip, and lay it on your new piece. So it's there, but in a small dose.

Or -- fold it like a bed runner but lay it under your pillows so you just get a bit peeking out from under. Hope you find a solution you love!

I hung my folksy quilts in my contemporary loft with whimsical oversized clothespin hangers, spray-painted metallic silver for a modern beat. Google search "clothespin quilt holder"; get a set of 2 for about $20.