Ok, to answer your questions
1. Yes they can tune your car with a wideband that reads lean afrs. I have an innovate wideband and the gauge goes up to 21.9. The sensor might register higher. They can also eliminate egr and the 5 wire 02 but like I said you need a different ecu (which they can supply and install) You might have 400-700 dollars or more into it til your said and done.
2. Several guys have tuned custom Hondas this way without egr and achieve the same or better mileage than the p07. So egr is not needed. Does it help with mileage? A-b-a testing would prove that but you might be hard pressed to find someone who has done it.
3.since they are talking about a custom tune the wideband they are quoting you on is probably the aftermarket one used for tuning. Depending on the tuning route that might include welding in a second 02 bung for it.
It's a shame they don't want to diagnose the issue at hand. Of course they don't make as much money that way. I'd call a couple other shops that are fluent in Honda and see if they'd be willing to help you out. Too bad you are so far away I'd offer you to drop it at my shop.
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Burn lean and prosper \\ //
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