Well, aren't you the ambitious one. Here is a schematic of the 2007 GT500, but it remains essentially unchanged through 2012 with the exception of changes to the heat exchanger.
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I think you'll need to source most of the hoses from either a wrecked GT500 or purchase new. Theses hoses are all expensive and you may be better off routing the intercooler plumbing with heater hose and pre-formed hoses with couplers. I don't see the thermostat housing mounted to the engine, so you'll need one of those too. Be prepared to grab your ankles if you need to buy new.
I see in your engine pic, that there is no oil cooler on the engine, so you may have to figure out what you need to do with the hoses for that octopus looking hose unit in the lower middle section of the schematic. It snakes back to the rear of the engine for the heater routing. Without the oil cooler adapter you will need to get some sort of adapter for your oil filter. BPS has one and there are probably others out there.
I think you should look for a radiator that fits the Galaxie radiator support in terms of size for the opening and has the inlet and outlet in the right places. I'd get one that has a shroud and a good sized electric fan. Knowing what I know about the GT500, I think the stock radiator will be too wide for the opening in the radiator support. However, your radiator support would probably allow for a taller radiator. You'll probably have to get a universal heat exchanger that you can get to fit in the space in front of the radiator. I would try to find the largest one you can install in that space. Frozen Boost has some universal intercoolers that might work for you. You'll probably have to fabricate your own brackets for whatever you do. You will need reservoirs for both the cooling and intercooler systems. It's going to be important for the fill caps to be higher than all parts of the cooling system. The OEM units might work for you, but you'll have to figure out some sort of mounting system for them. The mounting locations are integrated into fan shroud in the OEM fan unit.
There are a lot of options when it comes to intercooler pumps. Just do research on pumps in general because some do a better job of moving coolant than others when restrictions are present. Things like jacuzzi pumps may have a high unrestricted flow rate, but when restrictions are present, they can barely move coolant. That's true of most pumps, but some aren't even worth fooling with. The 13-14 used a larger pump, but it was mounted on the engine. You can pretty much mount it where you want, but make sure the pump manufacturer doesn't have specific mounting instructions. I say that because some of the more substantial pumps need to be mounted within a specified orientation and angle. I would also make sure it's mounted lower than the reservoir.
Good luck with the project. I'd love to see pics of the finished product.
@Buttinz has retrofit a 5.4 in a kit Cobra and he may have some helpful insights for you.
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