Hard to tell what's involved with out seeing it, but, you should be able to just put your travertine tile over all of the slate (no removals required) using fortified thinset. You may have to trim around the fireplace opening and sides of the hearth with pieces of the travetine. You can get a small tile saw at HD for under $100 that will cut the tiles so you can trim it nicely.

At my favorite tile store in our little town, there is a display fireplace with slate. They sealed it with a sealer (I don't know the brand) that brings out the BEAUTIFUL colors and really enhances it. It is super gorgeous! I have slate on one of my bathroom floors and I can tell you, a bit of steel wool and some warm soapy water will not hurt slate. I would recommend a sealer/enhancer after a thorough cleaning. I bet it will be gorgeous!

I'll take a couple of photo's of electric tomorrow for ya'll. I have two of them as well as two propane and two real. I seem to like two's :) Oh and two wood LOL Ok so I have a couple of fireplaces. I don't like the electric. They look fake. I'd like to remove both of mine but one is sort of built in so I'll have to wait (it's in a guest room) and the other in our family room is an old one that is half way decent, and puts out a bit of heat and we can't replace it with a propane because of the chimney height (if it's over 30' they can't do it unfortunately). The coolest electric I ever saw was in a house built in 1914 that was done with special light bulbs. It was so so so cool...obviously fake but in such a vintage way it was worth having. I wish I could find one of them...way fabulous :) Anyhoo, I'll take a couple of shots for ya'll with the cell phone tomorrow and see how you like a couple of electrics...and then fly down and take mine LOL

No you can not install granite, ceramic or porcelain tile over any type of tile. It needs to be removed and prepped for the new granite. If cement or concrete board is installed over the old granite then you can retile it without removing the original tile but there is no need. It is not a big deal to remove the old granite, you will be very surprised how easy it will come off. At 30 ftsq we are talking maybe an hour or two for 1 or 2 labourers with a chipping hammer on an average size fireplace to remove it. That seems to be a very high quote, however without really seeing the job it wouldn't be fair to the tile guy to dispute that quote. edit: I must add if the cause of the original tile cracking it will likely crack again. Is the quote include addressing the cracking issue as well?