Bricks, Masonry, Asphalt and Concrete - Correcting Multi_Clay Flue Drafting Problem

Need a tip on correcting a masonry chimney problem concerning a larger main level fireplace flue at the same level as a smaller basement fireplace flue [plus a furnace flue in the same chimney. The problem is that when the basement fireplace is used, it draws smoke back down through the main level damper.
We've been told to add at least 10" to the main level flue, but for appearance sake, we're at a loss. All flues have matching black rectangular metal screened caps with set screws holding them to the 1" of exposed clay tile.

What to do?

If cutting down a clay tile for extension, how does one make a presentable exposed masonry joint that will hold and last?

I would not extend the clay flue unless you are going to extend the chimney around it for support.
The best thing to do is fabricate a metal extension to match the flue cap and slip it over the flue.

Thanks!
I kind of figured that would be the best option. The only problem is finding a heavy enough guage of material to work with.
I still question whether the basement flue should not be the one raised, because it will still tend to try drawing combustion air through the main floor flue.
Ideally, we would provide combustion air to the basement. However, a remodel on this fairly older home is not in the picture.