A few comments for this already lengthy discourse. T4 is infinitely worse than T5 - on my only two connections from there onto Heathrow Express the link from T4 arrived as the 'connecting' train was leaving.
And yes, the tube is terrific.....unless you have to manage luggage up and down stairs in a majority of stations. Why not just have ramps for wheeled luggage? Hopefully this will be improved as Crossrail takes shape.
And, finally, for those who lament the connections at LHR - try living anywhere near JFK - no good public transport and constantly clogged roads. London is wonderful by comparison.