London Earls Court tube station

I'm traveling from Heathrow to Paddington and the obvious choice is of
course the Heathrow Express. As London is robbing my money already for
everything else ;-) I thought of using the tube instead. I am buying a
travelcard anyway so this trip would cause no extra expenses.

The only problem is that I have to transfer from Piccadilly line to
District. How hard is this to do at Earls Court, considering carrying a
suitcase or two and taking care of two kids (well, the Mrs will
help...). A long time since I was there and can't quite remember the
station! No problem with walking, just how are the stairs (escalator?)
and will it be very crowded at early afternoon (end June this will be)?
Or is it easier to change at Acton Town or Hammersmith? Or just waste an
extra 40 pounds for the comfort of the epress?