Use liquid nitrogen to cool the oil/gas mix and reduce the flow rate. The mechanism through which this would work is by the inverse correlation between visocity and liquid temperature.
The feasibility of this approach would seem to be highly dependent on the components of the leak. If the vast majority of the volume of the leak is methane, which has a boiling point of -161.6°C, reducing the temperature to the point methane becomes a viscous liquid would seem highly impractical. Without information about the components of the oil leak broad assumptions will have to be made. The stated data for light Louisiana sweet crude would seem to be a reasonable starting point. The pour point is cited to be -24°C by BP. A preliminary look at feasibility would determine the heat transfer required to bring the leaking fluid to that temperature.
Assuming the following:
Cp= 2.13 kJ/(kg*K)
leak rate = 5000 barrels/day
Oil temperature after traveling 1 mile through the riser (a guess based on 200°C out of well) = 100°C so deltaT=129°C
The required average heat transfer per second to the oil using these assumptions is then 2130 kJ/second.
Using liquid nitrogen to achieve this would likely incur significant losses in the process. One would guess such losses would exceed the heat transfer from the oil and so can't be neglected even in a rough feasibility sketch.
Saturated N2 thermodynamic table