The reason the size of the intermediate tank doesn't matter is that we're calculating pressure, which is force per square inch (psi), not total force. Pressure always comes from the total height of water, regardless of how much water there is (be it a barometer or the Oroville dam). Try not to think of it as 275 gallons vs 2,500 gallons, but rather the pipe itself.
Let's say you have a 2" pipe coming out the tower and 10psi of pressure in a 200" round tank. The total force in the pipe is 3.14 in^2 (pi*r^2) * 10 lbs per in^2 = 31.4 lbs. However, the total force in the tower is 314.15 in^2 * 10 lbs per in^2 = 3,141 lbs! That's why your tower needs to be so strong, but the pipe can still handle the pressure — it's a smaller cross section, and the pressure results in a much smaller force.
All that being said, with this setup your practical pressure will be governed by the intermediate tank's water level since it is likely your water tower will empty and water will be coming solely from the intermediate tank. If you go with this setup, I'd recommend installing a water
pump at the intermediate tank so you can maintain pressure at all times, but turn the pump off and save
energy when the water tower is empty.