Piccadilly takes forever. The correct answer is Lizzie line to Farringdon then change to circle etc to kings X. This will be much quicker. The Lizzie line train itself is lovely, air con, spacious, newer and cleaner. No Londoner would take the Piccadilly by choice any more.
Only issue is Lizzie line is often shut for engineering at weekends or has issues at the Heathrow end if the line.
Do not get the Heathrow express. It’s pointless, expensive and drops you off in the arse end of London. It’s main draw is unwitting tourists who think it’s any good.
There is also the consideration of taking a bike. Heathrow X will allow before 9 but Lizzie will not - on weekdays.