I'm not formally trained in this, but I've studied it some, and would offer these opinions:

If I understand you correctly,the 4 brass vents around your firebox, 2 to the right and left slightly above it and 2 to the right and left close to the hearth, are connected to a duct system that circulates air that has been heated by the fire. There may be a blower fan connected to the ducts to promote greater circulation of heated air into the room. Whether you have a blower fan or not probably does not matter.

So you want to cover these vents for cosmetic reasons in your re-design of the fireplace. I think there might be a concern if you are covering the vents with combustible material (wood), for 2 reasons. (1) If the air in the duct system gets very hot, it could degrade the wood over time. You might be able to avoid that problem if you stuff some insulating material into the ducts. (2) I think there is one other issue you need to consider to assure yourself that you are not incurring a risk of fire: the clearance between the edge of the firebox and the edge of the combustible material. If the latter is too close, it could theoretically catch fire. I do not know how minimum clearances are calculated, or even if there is a general formula for doing that. It depends on how hot the fire gets and how combustible the combustible material is. You might be able to sort this out on your own by making a really good roaring fire, letting it heat up for a good 15-30 minutes, and seeing how hot the vents get, especially the sides of the vents that are closest to the firebox. If they are too hot to touch or almost too hot to touch, then you know that you don't want to put anything combustible like a wood surround that close to the edge of the firebox. But if it gets just slightly warm to the touch, you can probably put a wooden surround that close without any danger of fire.

Incidentally, since heat rises, the clearance between the top of the firebox and any combustible material above it will probably be more important to be concerned about.

If I were you, I would consider a black metal fireplace surround, to replace the brass surround you have in place now and to extend out so that it covers the vents. Sheet metal fabricators can make one that looks like cast iron (which is too expensive), and that would blend in very nicely with your brick, and you would not have to worry about clearances. You can still get your wooden mantel, positioned one step removed around the metal. Of course, that's a matter of personal taste.

You have a really nice fireplace, and with a little careful planning you can make it even nicer.

Good luck.

The insulation you want is called "KAOWOOL" brand. It's ceramic fiber insulation and is used to line chimneys when woodstoves are installed into fireplaces. Put the Kaowool down into the ducts as far as you can and as close to the fireplace itself instead of at the outlet and you SHOULDN'T have any problems. You can get it from stove shops.
But WHY are you burning WAX logs instead of real wood? I can smell those things as soon as I go into a house that's burning them. The whole house smells like burning wax.

We live in an area with a high water table, and we have a deep ash pit that fills with water. Whenever we burn real wood, the pit takes on a smell that never goes away. We have filled the ash pit with cement, but the water still gets in, enough to create the smell. We are going to convert it to gas once we get the exterior hearth redone. Thanks for the advice.

You have to be sure to check the code for your area before you put any wood around your fireplace. An against code reno can screw you insurance wise if you ever did have a problem. As far as the vents go it's good your being cautious! I agree with chris on the insulation, or could you possibly incorporate some venting into your new design?

What you have is a heatolater type fireplace It is constructed and designed to use those vents Those vents dissipate heat build up which is part of the design.
If you close off those vents the fireplace should never be used again As an inspector I would require the damper to be welded shut so the fireplace could not be used. You may have other code issues using gas log sets in your fire place unless the original prebfab says it is ok to do so. You may not even be able to use a gas log set with the vents sealed again heat build up and dissipation still becomes an issue