In either case you have a 10" duct as the bottleneck in the trunk line. Expanding it downstream won't get you much in terms of flow. I'd go with Plan A.
Perhaps a more important question: Is the inlet attached to the fireplace somehow? You'll probably be disappointed if you just pull air from one room to another. The differential would be so small that you won't see much benefit. In fact, the air movement may make those rooms actually feel cooler.
When designing gas distribution systems, one must consider the demand of every appliance in order to find the minimum pipe sizes.
But, to answer your first question, there is little disadvantage in using larger pipes (except for cost and space). It is very likely that the 1 in pipe will be sufficiently large.
The calculations needed require you to know the lengths of the pipes and the amount of gas used by each appliance. Also, you need to know the gas pressure fed into your system, and the required pressure at the appliance. For low-pressure gas systems (like are in most houses), pressure drops linearly with distance. Tables (generally in the fuel gas/housing code) state the pressure drop per distance with various pipe sizes and flow rates.
So, one consults these tables and calculates the pressure delivered to each appliance with your pipe configuration (assuming that all appliances are operating simultaneously). If the delivered pressure is above the minimum required, then all is well.
The relevant regulations (including tables) are copyrighted, so I'm posting them here. They are likely available in your local library.
Be sure to read up and follow all relevant regulations, including performing a pressure test of the newly installed pipes, in order to ensure that the installation is safe. (Also note that high pressure testing will damage regulators in your appliances, so close their shut-off valves before the test).
Best Answer
The child's balloon is a great analogy for the gas piping system in a house. But rather than having been tied off with a knot, the neck of the balloon is still pressed to the lips of a parent with infinitely large lung capacity. (The gas piping is not a closed vessel, but is connected through the gas meter to a vast reserve of natural gas in the supplier's distribution system.) If the parent steps outdoors into a cold ambient, using their diaphragm to maintain steady air pressure inside the balloon, the balloon won't shrink. It's true the air inside the balloon will contract -- it'll become more dense as it cools -- but some of the infinite supply of air in the lungs will flow in to make up the difference and maintain the volume or size of the balloon.
What would happen if the child's balloon were not a round globe, but instead a very long tubular balloon used for making art? If just the end of the balloon were put out through the window, would the outdoor part shrink while the indoor part remained unchanged?
Pressure in a closed gas pipe system, ie where the meter is hooked up but at the moment there's no flow, will be equal at every point in the system regardless of the temperatures of various sections. The density of the gas will vary with temperature but its pressure will not.
But static pressure is not the factor that causes us to use varying sizes of pipe.
When the appliance valve at the end of the pipe opens and gas starts flowing, then yes, the strict engineering answer is that ambient temperature affects the pressure drop. Engineer's Edge provides the following equation for calculating pressure drop of a fluid flowing in a circular pipe:
The relevant piece here is rho, the density of the fluid. The density of natural gas is inversely proportional to temperature; as the gas gets colder its density increases. Because rho is in the numerator, an increase of density caused by low temperature leads to increased pressure drop in the pipe. That could make necessary an increase of pipe size.
Fortunately, for small buildings matters like lumber, wire, and pipe sizing are often handled by following prescriptive tables rather than by developing site-specific engineered solutions. Though the pipe sizing tables don't explicitly state it, I believe we are to assume that the prescriptive tables include allowances for worst-case conditions of cold temperatures, rough and rusty pipe walls, and so on.