Just reporting back the first half of my journey.
- Arrived in terminal 2E building K. Building K is where the exit to the RER train station is.
- tried to go through transit security in 2E- K to use their lounge but my connecting flight is in 2E-M so they redirected me to 2E- M
- took the train to 2E- M.
- went through security clearance there
- went to the lounge, had a shower
- left the lounge. Had to start backtracking. The sign was not obvious but once you start backtracking you will see the exit sign leading back to 2E-K.
- took the train back to 2E-K
- cleared immigration
- cleared the baggage claim and customs area
- walked to RER train station
- whole process to get off plane, shower and get on RER was about 45-60 min. But your time could be longer if you don't have a passport with automated control (eg. Canada, USA, UK etc)
Will report back once I return to the airport.