Piccadilly 73 Stock on District Line at Ealing Broadway

Yes exactly, T400 182+199 doing Ealing Broadeay-High Street Kensington.

that's would be first time the tube stock runs to High street kensington station

This one ran from Heathrow to Olympia via High Street Kensington.
It ran in service between Earl's Court and Olympia.

I presume you mean the 73's specifically?
Piers Connor in his "The 1938 Tube Stock"(page 88) says it was common when trains were transferred from the Northern to the Piccadilly, that they were the 'wrong way 'round'.
They were turned by using the Kensington triangle, then to South Kensington, reversed and off to Northfields.
If you haven't got this book, get it, brilliant pictures and full of information.
Did you know it was proposed to extend the Bakerloo to Dartford? "...Camberwell to Peckham Rye, surface to join the SR to Nunhead & Lewisham. It would take over the lines to Dartford via Bexleyheath."

I have a picture when one took a wrong signal at Hammersmith then another at West Kensington so had to go to High St Ken to reverse this was about 2003

Sometimes when a 67TS came back from Hainault to Northumberland Pk it was wrong way round and a move was arranged to reverse it via Piccadilly & High St Ken then back to Northumberland Pk.