Since you say the fan doesn’t change speed, then you know that the fan system has a fault.
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Unless you like tinkering with cars, it would be better to fix the hydraulic fan system than to convert to electric. You will have to go somewhere that is used to working on the LS or the Jaguar S-Type. Often they want to replace the whole system rather than figure out what is wrong.
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Since you say that you see steam coming off the degas bottle, you know that it is cracked. It will have to be replaced. Get a new one from Ford. Do not get the aftermarket one. It is thinner and lasts half as long as the Ford part.
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Since the engine has been overheating (due to the problems above) you can be sure that the plastic parts of the radiator hoses and of the thermostat housing are cracked or will crack shortly. I recommend changing all of those too.