Fat mud or backer board for tiling over brick fireplace?

[BigRedd]

Looking to tile over a floor-to-ceiling brick fireplace. We will be tiling not just the face but also a few inches of each side as the outside corners are important to the design. I've uploaded a picture, which is hopefully worth 1,000 words.

Bottom line up front: in my situation, (1) would you use fat mud or backer board (or something else?) and (2) whichever method, please provide broad strokes of how you'd go about it. Thanks!

The situation:

You can probably see in the photo that the face plane of the fireplace isn't flat (never mind plumb). The picture is a little distorted and makes it look worse than it is but the face plane is indented in the middle like it's wearing a too tight belt, by nearly half an inch. It seems like that would be too much thickness (especially with the mortar joints adding to it) to just put on a couple of coats of thinset and start laying tile. So to flatten and plumb, I've looked into either fat mud or backer board.

It certainly seems like the pros generally prefer the fat mud route but I have three reservations:
(1) The outside corners. It seems like it would be difficult even for a pro to get plumb and parallel outside corners with fat mud.
(2) The product data sheets all talk about using wire mesh or similar for structural support of the fat mud but I have no idea how it could be fastened to the brick/mortar; and
(3) I'm a newbie to fat mud and would be hesitant even if I didn't have the outside corner problem.

So I'm leaning toward using backer board. I've seen plenty of pro feedback that is skeptical of fastening backer board to brick/masonry. I'd welcome feedback on the following:
1) I'd first use mortar to fill in all the voids in the brick and possibly even to do some minor leveling/plumbing. I'm not pressed for time so can let it set as long as needed to reach full strength.
2) I'm also considering using furring strips, which could be shimmed level/plumb and fastened with construction adhesive and Tapcons. Then attach the backer board to the furring strips. Assuming it could meet code having the wood furring strips close to the fireplace (we're going with a gas fireplace insert, so should be good), do you guys like the furring strip option better or worse than attaching the backer board directly with thinset and mechanical fasteners? I am aware of the preference to put the mechanical fasteners (I lean toward Tapcons) into the mortar rather than the brick.
3) A third option I thought of, which may be the best or worst of both worlds, is to install backer board on the two sides, taking care to get the leading edges on the outside corners to be plumb and parallel to each other. Then I could fat mud the face using the leading edges of the backer board as screed guides.

Any/all help appreciated. Thank you. This is a great forum.

[Davy]

Tap cons can be used to fasten the lath to the brick. Add flat washers to the Tap cons if needed. After the lath is up, you can screw a straight 1x4 to the sides of the fireplace and using the edge as a screed like you said about the Hardi board. After the face is mudded and set, pull the 1x4's and screw them to the face through the new mud.Then you can mud the sides. Your mud will be as straight and plumb as your 1x4's.

It helps to get a little practice doing mud work before jumping in with both feet. So I can understand your concern.

I prefer the screws go into the brick instead of the mortar.

[BigRedd]

Thank you, Davy. Any advice on Tapcon spacing for fastening the lath? Also, do I absolutely need the lath? I just read another thread here where the advice was that, if the brick hadn't been painted (it hasn't), then one could skip the lath. Not trying to cut corners but also would like to avoid unnecessary work.

Thank you for your feedback.

[Davy]

I've mudded many small fireplaces without lath. I'm talking just 12 inches around the firebox but on yours I'd wrap it with lath since it goes up so high. I can't say if it's 100% needed or not but fat mud doesn't have much bonding strength. It helps if it locks into or around something. I'd space the screws about every 6 inches and overlap the lath 2 inches. Extra screws may be needed in places where the lath bulges out. Lath has at least doubled in price in the last 2-3 years.

[Dave Gobis]

I have done a bunch and always lath. The argument could be made the unpainted brick should be good enough but have never been a probably good enough kinda guy.

[John Bridge]

Concur on the lath. Brick structures aren't all that stable.