I would update the face with some sort of stacked stone with a rustic distressed mantle

For a cohesive design, the style of the fireplace needs to compliment the style of the finishes and furnishings around it. For example, this facade can be ok with transitional or simple-line pieces, but it wouldn't do in a rustic, traditional or contemporary setting. So it all depends on what your personal style is and what you are planning to do with the rest of this space.

Changing this fireplace surround will be a big expense. Before you go that route, I would paint it. 2 choices-dark color so the mortar does not seem so prominent or paint it the same color as the wall so it is less of a focal point. You could also add a mantle. Know that once you paint it you can never go back.

It turns out, we cannot replace it at this time. We are seriously considering painting it, however I have never been a fan of painted brick. What if we just put a big painting over it?

And we are definitely adding a mantle.

Obviously it is your decision, but you will still be stuck with the stains. I tried everything to clean fireplace bricks and still ended up painting it. Good luck.

Have you tried Easy-Off oven cleaner for the bricks? That is what I used to use when I had brick.

And "wash" the brick with paint, don't "paint" it.

I don't know what the rest of your house looks like, but I kind of like the fireplace, it's very midcentury style. If your decor is in that style I think you could get away with just painting or washing it.

Add a reclaimed timber mantle.

Give it a pass to make it match the wall color, add a mantle, and put some art over the mantle; if you can't afford to change the brick right now. Once brick is painted it's pretty hard to get the paint off/out of it.

You may also consider simply sheet rocking over the bricks, and adding a pre-fab mantel. The project I've attached is just exactly that. The 'back' portion of this fireplace is what your existing brick would like with a layer of sheetrock over it...

Keestey- the picture you attached is really nice. If I knew my room would look like that, I'd paint it for sure!

M3459. - How does one "wash" the bricks with paint?

You dilute the paint: half water/half paint. You then paint the bricks with a brush and wipe off the paint with a dry cloth.

Don't know what you used to try and clean the bricks, but here are a couple of tips to clean fireplace bricks:
http://www.howtocleanstuff.net/how-to-clean-a-brick-fireplace/