LED switching: Circuit reacts unexpected
You picked a transistor with a transition frequency of 100 MHz, according to the NXP datasheet. That's the point where the current gain of the transistor drops by 3dB.

Your application requires a much higher bandwidth: A step has infinite bandwidth; a step that's rounded off for no longer than 6 ns has at least a 2/(6 ns) bandwidth, i.e. > 100 MHz.

So, wrong choice of component.

Then, the inductor in parallel: congratulations; you've built something to produce negative voltage spikes! These will indeed turn of your LED quicker, but do form an oscillating circuit together with the capacitance of the diode and the transistor junction in reverse bias ("LC-Schwingkreis").

Also, these spikes might destroy your LED - its datasheet clarifies that it's NOT designed for reverse bias and you're building voltage spikes that are in amplitude much higher than your supply voltage.

This circuit won't do.

Switching a 2A load like your UV LED requires something a little beefier than your cute little BC847. Look for fast FETs and RF BJTs, as well as high-speed drivers for FETs to get a feeling for what is hard and easy, and what appropriate components might be.

Also, where did your SPICE model of the LED come from? Diodes have a parameter called storage delay time, which is basically the time it takes for existing minority charge carriers to recombine (and emit light). At an initial current of 2A, I'd be surprised if this delay wasn't visible on the scale of nanoseconds – especially since your LED isn't meant for high-speed communication, but high-power illumination. I could imagine that even if you manage to turn off the current through the pins of the LED in less than 6 ns, physics simply not allow you to stop photon emission in time. You'd need to characterize your LED with a >> 100 MHz bandwidth oscilloscope and a reliable off-switcher yourself, since OSRAM is not supplying that data (you could simply ask OSRAM, but I doubt they'll give you that data; it tells experts too much about how their LEDs are made and which tolerances they have in production). 

The crassest mistake you made however was your choice of opamp – that thing has a gain-bandwidth-product in the single-digit megahertzes; I don't see how you're expecting that to drive any transistor fast enough to reach anything close to 6 ns edge duration.

So, clean slate: It's clear that you've read a bit on circuits to quickly shut off diodes (at least that's what I guess from where the inductor comes), but you haven't done the math with the components you have. You can't "tinker" together something that works on nanoseconds timescale – it simply won't work. This thing will, in the end, require you to do a high-speed PCB layout, with components that can do what they need to do individually. That will require you to calculate what they need to do before you start simulating.