Basically you are trying to balance your new ducts with respect to your old ducts by sizing the new ducts. If you make a mistake or if your relative cooling loads (office vs rest of the house) ever changes, your only recourse would be to replace the ducts.
My preference is to size the ducts as large as reasonable possible (without increasing cost too much) and use a damper to tune the airflow ratios. Since you have 12" duct and a place to attach them, just get a damper like this:
http://www.grainger.com/Grainger/DAYTON-Round-Balancing-Damper-2TFY1?Pid=search
An uninsulated unshaded west wall in Texas can probably generate a very high cooling load in the afternoon.
International Residential Code (IRC) says the maximum exhaust duct length is 35 feet. However, it also says that this length can be overruled by the manufacturers instructions, if the instructions are provided to the inspector.
2012 International Residential Code (IRC)
Chapter 15 Exhaust Systems
Section 1502 Clothes Dryer Exhaust
M1502.4.4.1 Specified length. The maximum length of the exhaust duct shall be 35 feet (10 668 mm) from the connection to the transition duct from the dryer to the outlet terminal. Where fittings are used, the maximum length of the exhaust duct shall be reduced in accordance with Table M1502.4.4.1. The maximum length of the exhaust duct does not include the transition duct.
M1502.4.4.2 Manufacturer’s instructions. The size and maximum length of the exhaust duct shall be determined by the dryer manufacturer’s installation instructions. The code official shall be provided with a copy of the installation instructions for the make and model of the dryer at the concealment inspection. In the absence of fitting equivalent length calculations from the clothes dryer manufacturer, Table M1502.4.4.1 shall be used.
I couldn't find anything that says the termination has to be a specific height above the ground, just that it must be 3 feet in any direction from any openings into the building. And that it should have a backdraft damper, and no screens
2012 International Residential Code (IRC)
Chapter 15 Exhaust Systems
Section 1502 Clothes Dryer Exhaust
M1502.3 Duct termination. Exhaust ducts shall terminate on the outside of the building. Exhaust duct terminations shall be in accordance with the dryer manufacturer’s installation instructions. If the manufacturer’s instructions do not specify a termination location, the exhaust duct shall terminate not less than 3 feet (914 mm) in any direction from openings into buildings. Exhaust duct terminations shall be equipped with a backdraft damper. Screens shall not be installed at the duct termination.
The code also says that the ducts must be 4" smooth walled ducts, and sections can't be attached using fasteners that protrude into the duct more than 1/8".
2012 International Residential Code (IRC)
Chapter 15 Exhaust Systems
Section 1502 Clothes Dryer Exhaust
M1502.4.1 Material and size. Exhaust ducts shall have a smooth interior finish and be constructed of metal having a minimum thickness of 0.0157 inches (0.3950 mm) (No. 28 gage). The duct shall be 4 inches (102 mm) nominal in diameter.
M1502.4.2 Duct installation. Exhaust ducts shall be supported at intervals not to exceed 12 feet (3658 mm) and shall be secured in place. The insert end of the duct shall extend into the adjoining duct or fitting in the direction of airflow. Exhaust duct joints shall be sealed in accordance with Section M1601.4.1 and shall be mechanically fastened. Ducts shall not be joined with screws or similar fasteners that protrude more than 1/8 inch (3.2 mm) into the inside of the duct.
NOTE: Always check with your local code enforcement agency before begining any project, as codes vary from location to location.
Best Answer
Consulting with an HVAC technician advised:
left duct
from the fireplace just below the first floor subfloorright duct
just above the wye on the first floorleft duct
using 6" round B-Vent. The technician pointed out that it's key to match the existing brand (I have Ameri-Vent) so that the turn-and-click attachments are the same.right duct
and fireplace, capping each with a sheet metal & silicone end cap.