Well, you'd need a turbo that would be big enough to have lag, so a GT35 would probably be your best bet. But that turbo is ~1300 and then you'd need a good manifold, downpipe/testpipe, intercooler, piping, fuel pump, fuel injectors, etc. That would be hard for ~$4k, mainly because you'd need a great manifold and it's hard to find any good ones used.

You could run a TSI manifold with a GT3071R but you wouldn't really need the nitrous to help with spool, actually what is your nitrous window now? You COULD use it at lower rpm but it would be killer on your transmission.