Your hardware should be capable of at least 270bhp. 240bhp is more like what you'd see at Stage 1 with standard hardware.
Are you saying a k04 conversion 'gains very little HP for the expense'?
I'm not sure who's been advising you or what you've been reading, but I wouldn't call it accurate. A k04 on your car would give you upwards of 340bhp. An S3 intercooler and injectors would be more or less essential if you went k04. But not if you're staying k03. Intercooler maybe, but definitely not injectors.
If someone's telling you your car should be putting out 240bhp, stop listening to them. If your car is actually putting out 240bhp, there's a fault.