I agree you would need to leave some stone exposed as protection from the fire. You could cover the exposed stone with something else, I love the cobble stones used in the link below. There are 2 other fireplaces which illustrate quite nicely what yours would look like- numbers 4 and 11 in the same link. Hope that helps!
http://www.bhg.com/decorating/fireplace/styles/stone-fireplace-design-ideas/

The code requires 12" minimum non-flammable surface to the sides and 16" to the top of the firebox (IBC)... Assuming that there is building code enforcement. Laminating slab over the existing stone is doable, a parge coat of mortar to achieve a smooth surface would be necessary. Talk to your contractor and the mason. Paneling the upper section and adding a mantle are fairly straightforward. The integrity of the existing stone is paramount. One thing to note, most electricians will not mount a flat screen to masonry. They want the screen mounted directly to structural studs. One way to do that is to create an overhang above the mantle, supported by columns. This pushes the over mantle into the negative space of the room and adds architectural interest to the wall. I'll try to post a picture of a current project later today.

Thank you both for the advice and ideas.

We have the same Indiana sandstone fireplace and have been looking at updating the look. Our stone appears to be just a "face" type stone and thus easier to completely remove than you might think. You may want to consider a fire rated tile or marble to meet building codes around the fire box itself and then build your mantle/surround from that point . This would also give you the option of providing proper support and chase-ways for the television mount and wiring.

With wood paneling and mantle you could use tile or slate for the non-flammable surround. It depends on what style you want.