I must say, I'm not a huge fan of the noise but I'll see what I can do about that!
The 2.0 LSJ is a GM engine from the states very closely related to the 2.2. It produces 200bhp with its standard supercharger/pulley.
The internals on the 2.2 are limited to about 250bhp. At which point for significantly more power you'll start looking for a sand cast ported head, rods, pistons etc. Given the cost of doing all that to the internals it appears to be cheaper to drop in a crated 2.0 LSJ engine (which is almost a straight swap) as that is cheaper and has the proven higher spec internals already.
£5k to supercharge the 2.2 to a little over 210bhp or perhaps £1,500 to get a200bhp factory spec engine from the states, spend a bit on pulley, charge cooler and chase 300bhp for the same as it costs to hit 210bhp with the standard 2.2.
There are a few people currently experimenting with the LSJ engine, but that's as far as its got at the moment.