The low pressure pump is certainly a potential issue. You're not the first person to suggest that.
I may well uprate that along with the turbo even if the car continues to behave in the meantime.
It is a common issue usually caused after a remap from all the reading I've been doing although not with every golf or vag car but worth replacing. Dan_fr mentioned I need to get a 200 bar fuel rail pressure sensor to help with requested fuel so keep that in mind when going K04 as it makes perfect sense from his advice to replace this although tuners won't tell you this and scream every little they can out of the weakest link also the RS4 fpv will aid also but tuners say not essential. Remembering we have old cars and some lpfp maybe fine where as others will be cutting close to failing.
Yes, very true. I have the RS4 return valve in there now so that's one thing ticked off. Apparently there was a revision to the LPFP - not sure exactly when - but mine is the newer pump according to Steve at Statller. Although as you rightly say, parts get old so it doesn't necessarily mean mine is functioning perfectly even though it's a revised part.
I'm also going to get the fuel filter replaced when it next goes in, these are not deemed as servicable by VW as I'm sure you know, and I've no idea whether it had ever been replaced before I bought the car.
Slowly but surely getting there!