mmmm....
Armour 15 16%
M6 17%
J4 5%
PP7.8 (must be equal to M +1.8 for Meson screen) 7.8%
Engineering crew 0.596%
J fuel 40%
PP fuel 7.8%
purification 0.717%
Bridge 2%
Command Crew 0.1%
Service Crew 0.6%
equals 97.613% payload = 2.387%
plus
9fib computer 26T
command staterooms 6T
T Meson 8000T
factor 9 Meson screen 40T
gun crew 176T
Power for 1200 ep 1200T
Fuel 1200T
Purification 18T
Payload equals 10666T
Therefore Min ship with agility 6 armour 15 T meson and factor 9 meson screen equals 10666/0.02387 = 446,838T
(or to put it another way, isn't going to fly)
You've done something wrong math wise...
Additionally, FPP isn't essential, and I put the PP slice for the weapons and defenses into the defenses; they are, semantically PAYLOAD.
And the T meson is 7KTd, not 8, until you add the 1200 (not 1000) Td for power plant (and then you need to add the additional PP fuel).
I did make a mistake, tho, as I should have used PP6 or reduced to M4 Agl 4.
M4 makes it work, and frees up a few extra %... it's only 11%.
Also, rounding Command, maint and drive crew up to 2% hull at TL15 is generous for DO staterooms.