The tallest counter-depth units are from KitchenAid/Whirlpool and are 72" tall. When we did our kitchen remodel in 2006, we went with a KitchenAid counter depth at 72", and there is about a 0.75" gap above it where the wood cabinet is. I would suggest trying to do something similar in your situation. Replace the current cabinet above the 82" with a larger one that would come down to 73". But you'd have to see if they can still match the style and color so it all goes together. If not, then just a cut piece of wood that is color stained to match would be the next option.

Thanks Ci_lantro for the code info! I looked up our local code and it's only 6 inches from the firebox for mantels and trim and combustible materials within 12 inches can only protrude an 1/8" for every inch away from the firebox. We have appx 22" of space now. Good info to have it we plan on putting the trim around it. We peeked behind to see where the drywall ends. We could take out the first row of brick but there is no drywall after that - and my drywall skills aren't such that I want to get into that mess (or pay someone to do it). Thanks everyone for the ideas. We have plans in the next week with a friend in the fireplace business and a family member familiar with the code so we'll pick their brains with some of these ideas!

An alternative idea: This probably won't work if the wainscot if a thin luan-type of sheet good. If it is real wood, it may work if the bow has some movement to it. Drive an oversized hole in the baseboard. Large enough where the diameter of the hole does not catch the threads of the screw, but small enough where the countersink of the hole still catches the screw's head. Run a deck (NOT a drywall screw) screw through the hole and if the wainscot is of sufficient thickness, the threads will grab the wainscot and pull it towards the baseboard. The patch and paint the screw holes in the baseboard.

Unfortunately, I don’t see an easy way to hide those gaps. If there was a front overhang for the countertop, you could easily apply a small piece of trim molding on both sides. However, with no overhang, the problem is how to esthetically terminate the top end of the trim. You’ll have to decide if having an exposed top end to the trim with some kind of bevel is acceptable. I wouldn’t try to build up the surface, or to caulk into those cracks. It wouldn’t look very good, and would just draw attention to the issue. It would be better to just learn to live with them, than to do such a bastardized fix.