Smoke rising in a flue travels in a circular pattern so the corners of your clay tile are effectively useless which must be deducted from the over all total. Really it isn't so much the area as it is the location of the chimney in terms of surounding topography, prevailing winds, etc and most...
It seems a simple mortar with polymer bonding adaptive would be sufficient to close off joints. The freshly TP joints then become your monitor for any future movement as these are the stress release areas.
Most clay liners average maybe 10 1/2" x 10 1/2" effective inside area for a nominal 12 x 12 flue.
A round flue is more efficient due to the nature of fluid dynamics and most drop in flue systems measure the flue inside diameter not outside diameter like is done on the clay tile so the actual...
Frankly if someone wanted me to come out to give them free advise so they could shop my ideas to others, I'd tell them to take a hike. Goodd advise is rarely free.
The purpose of your liner is and a dead ain't space around it is to provide an impervious surface for flue gases to escape along and to prevent heat sink into the surrounding masonry. More importantly though is that a cracked tile can fall in during a flue fire blocking the flue which can create...
Your problem could be the result of improper foundation flashing especially if the water comes over the top of the foundation. This is a sure sign of problematic flashing