A couple things to consider when choosing your method…
When you look at those cool photos/videos of F-14’s taking off from aircraft carriers at night, you can see that the exhaust is more of a pulsing plasma type effect, very hot and very powerful. Kind of a repeating, pulsing wave of hot plasma. Not that you can’t get something kinda like that with particles, but I think you might want something a bit different.
Also, one of the bigger challenges, IMO, is the shading. The effect you see is very much like heat waves rising off an asphalt road in the hot desert. Kind of a blurring of the background due to the hot air bending light.
So once you get the shape figured out, the key issue in believability will be the pulsing, blurring effect. In real life, that’s due to the transparency of the air being modified by the heat and the burnt fuel, which changes the IOR of the air. Or something like that….
So I’d spend a lot of time working with transparency/alpha/IOR to get it just right, so you get some blurring, but also you can see the pulsing plasma effect.