Yeah that "backpressure is good" myth drives me crazy. Backpressure just adds more pumping resistance and reduces power and mpg. It's all about scavenging and velocity. Where it is most critical on a normally aspirated engine is the header primary tube size more than the exhaust pipe size. High velocity in the primary tubes keep drawing on the exhaust port more than low velocity so it helps scavenge the spent exhaust better making more room for fresh air/fuel mix in the cylinder on the intake stroke which make more power. The lower the rpm range and smaller the engine, the less velocity coming out of the exhaust port there is so a smaller primary tube will be needed. The bigger the engine or the higher the rpm range the bigger the primary tube needs to be to move enough air for the engine combination.
I bought a program called "pipemax" that is designed to figure out header tube sizes on race headers. It lets you plug in all your engine specs and rpm range and it tells you the best primary diameter & length, the best collector diameter and length and loads of other info depending how serious of a combo you are working on. If you want stepped headers, it tells you the dia. and lengths of the steps. If you want to use a merged collector with a cone shaped colletor it tells you those dimensions too. Anyway, that is way beyond what we are talking about in your application but the concepts are the same.
One thing to think about on yours is that the 2" exhaust pipe will have higher velocity which will probably raise the pitch of the exhaust note... I think the slower velocity of a bigger exhaust pipe will deepen the exhaust note. I guess if it sounds funky with the small pipes, you can always go up in size later. Or, you could shoot for a middle ground of 2 1/4"
Here's a pic of the headers I built a while back for my drag car using pipe max to figure out the sizes/lengths. They are 1 7/8" to 2" steps with merged colletors.
