If you were willing to put a few nails through the front (you can later fill the nail holes with oak colored wood filler) to hold it, I would say to use a good construction adhesive like Liquid Nails. If you can figure out a way to clamp it, then Liquid Nails is also the way to go. You could try contact cement, which grabs instantly, but I'm not sure it will have enough initial holding power on a 3/4"(?) oak board (by the way, if the paint is a semi-gloss or gloss you should rough up the surface with sandpaper first). If none of the above is feasible, you could try to assemble the pieces off the mantel using construction adhesive and clamps and then slip it on. In any event, if you do use the adhesive do not put it on too thickly or the pieces won't fit together properly.

I like some of the suggestions on the Kylie M. Interiors web site on the topic of paint that goes with oak. You could use her suggestions as a starting point and then adjust depending on your lighting and other elements you need to consider (furniture, etc. in the room to be painted). To avoid playing up the wood you're on the right track in sticking with a warm color, but it definitely doesn't need to be brown to be warm and cozy. If your husband likes rustic/traditional, I'm guessing painting the trim is not an option. My husband much prefers wood trim as well, and I've definitely come to appreciate its beauty way more than I thought I would (our main floor trim is stained fir). It definitely adds a nice warmth and gives personality to your home.

Paint the wall and wainscotting the same color. And before you buy a brown rug, maybe consider other colors? You've got a lot of brown already and something with a little more life would add a lot to your already nice room. Even the little peek of orange in the existing rug looks very nice.

You can use most colors, with your stained trim, except yellow shades,. Blues, greens, aquas, whites etc all go very well, with stained trim.