The chances are good that your 13" lens can be adapted to a Compur/Copal/Prontor #1 shutter. The 18" might be adapted to a Copal #3.
You might be better off leaving your Ektanons on the shelf and looking for a 12", 13" or 14" process lens (Apo Artar, G-Claron, Apo-Ronar, Apo-Nikkor, ...) in shutter and an 18" process lens (Apo-Ronar) in shutter. It is very often the case that a lens in shutter can be bought for less than a shutter and adapters to hold the cells of the equivalent lens received as a gift.
By the way, although EKCo bought shutters from Ilex for mounting some of their lenses, e.g., f/6.3 Commercial Ektars, these shutters' threading is not to the Ilex standard. Other makers' lenses won't fit a Kodak Ilex shutter and Kodak lenses made to fit a Kodak Ilex shutter won't fit a non-Kodak Ilex shutter.
On this point, I have an Ilex #3 Acme that has a Kodak Anastigmat jammed into it. When I decide to use the shutter I'm going to have to pay someone to extract the lens' cells. A previous owner was an ignorant fool.