I have an 07 bike. The listed part number is 37870-MBG-003 and it's about 50 to 60 bucks
The 2012 (and maybe others) has a part number of 37870-KRJ-901 and cost 20 bucks.
If I am going in anyway, do I want to install the newer model which looks just like the old model, or do I install the old model.
Use the part that's listed for your bike unless the parts fiche says it was superseded by another. The part for the newer bikes will look the same because the assembly where it's installed hasn't changed, but you're going to be chasing your tail if it's different internally. If Honda is carrying two separate versions of the part, there's a reason. (It's like using a class 8.8 bolt in an application that calls for class 12.9 just because they look alike except for the number.)
I am chasing a poor fuel economy issue.
The amount of gas your bike consumes is governed entirely by how much fuel gets squirted through the injectors. Assuming you're not heavy on the throttle, there are a few things that will have an influence on that:
Sticky Injector Valves. If there's crud built up in your fuel system, some of it could have made its way into the injectors and is either preventing the valves from closing fully or making them lag a bit. Add your favorite fuel system cleaner (I use half of a 16-ounce can of Sea Foam) to your next two tanks of fuel and get the bike out for as many highway miles as you can and run it down as close to empty as you're comfortable (one bar is fine). Ignore the fuel economy of those two tanks, but pay attention to what it is for the two or three that follow.
High Fuel Pressure. If the fuel pressure regulator has failed (don't think I've heard of that happening) or has been intentionally adjusted high (which is what the Turbo Tom replacement is), more fuel will end up in the mixture than intended. I don't have any information about what effect the TT regulator has on fuel economy, but I'm pretty sure it's been discussed. Either way, these are probably not the droids you're looking for.
Overactive Cooling System. On older bikes, this is the classic stuck-open thermostat that leads to the coolant being too cold and the ECM trying to get the engine temperature up by adding fuel to the mixture. You've been through that already, but if you feel like testing the replacement again, the thing you want to watch for is that it's closed by the time the water temperature falls through 175. Thermostats, being mechanical beasts, may not behave the same way in both directions.
Bad Data to the ECM. Under most conditions, the ECM tries to maintain a 14.7:1 air-to-fuel ratio. The amount of air in the intake is calculated on temperature and pressure, which are measured by the IAT and MAP sensors and the final AFR is nudged toward rich if the ECT says the coolant is cold. It is entirely possible for a sensor to fail and still give plausible readings (e.g., coolant temperature reads 150 when it's actually 180) and the ECM will act on it as if it were gospel and not throw an error. The TP (throttle position) sensor also figures into how the ECM changes its behavior to meet emissions standards, and you could have a situation where the mixture remains ideal where the rest of us have it go lean and consume less fuel. Check all four sensors using the procedures listed in the manual.
HTH.
--Mark