The first piece of hardware is the Dorbin 97AS Black Pile Adjustable Double Door Equipment 84" Length As seen here:
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This piece of weather stripping employs an extruded aluminum channel into which you will slide the black pile weather seal insert to create the effective seal between the two doors. The elegant portion of this piece of hardware is that after you have routed the channel in the edge of the wood door you employ springs underneath the extruded aluminum holder and when you use the screws to install the channel to the edge of the door you are able to control the projection Of the seal by how much you turn the screws in or out.
And yes you were very accurate to predict that you would have an interrupt where the hardware projects from the door and I would suggest that you use this piece of much smaller bristle style weatherstripping to account for that small interrupt period this piece would in effect act as a lock strip. An example of this hardware would be the Pemko 5025ASB 12" BL Mill Finish Aluminum Mortise Retainer with Black Soft Brush insert and can be seen here:
I have put together a quick hand sketch of what the concept would look like as seen here :
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