Hmmm.
For mpg purposes, the benefit of a turbo is that you can get more power from a physically smaller engine. It weighs less, and depending on how the computer is programmed, you could potentially be light enough on the gas pedal so it will consume little fuel when you don't need the turbo's added power.
So instead of selling you a car with a 1.8 liter engine who's best mpg will be limited by that (higher) displacement, they can sell you a 1.4 liter with turbo. It can burn less fuel than the 1.8 at low output, and when you want to move, 1.4 + turbo is at least as powerful as 1.8 without, if not peppier. Like the Chevy Cruze and Sonic.
Whether it's worth it to spend the time and money in an effort to gain mpg, is very doubtful. Because you're not going to reduce the displacement of your engine if you just add a turbo. You would be adding turbo power to it, along with the turbo's capability of jamming more air and thus more fuel into the same engine. Good for speed, likely not good for mpg.
Your other concerns - oy vay, if you don't mind a couple words of Yiddish. The EX tranny is geared low, for higher rpms. Not your friend if you want more mpg. And yes the computer runs the lean burn capability. If you want HX performance I say you'll need an HX tranny, computer AND wire harness, plus the correct wideband oxy sensor.
You could sell the HX to someone who wants to finish ricing it.
One thrifty approach is just to drive what you have, with the best technique you can put into it. Reduce moving losses with thinner oils, higher tire pressure, LRR tires when it's time for new ones, aerodynamic projects so you're fighting less wind resistance. A fuel cut switch so you can engine-off-coast easier than by turning the key. Killing the engine at any rolling speed reduces rpms really really well, which is why we do it. Only with a standard of course, an autotragic just won't take it.
If you want a serious project, look into things like Megasquirt that might let you map your own lean fuel mixtures and modify the ignition advance, etc.
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Coast long and prosper.
Driving '00 Honda Insight, acquired Feb 2016.
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