Not a challenge that I would relish in the time you have available but I think it is doable. It is altogether different getting to Selhurst than it is to Craven Cottage - south-east rather than south-west London - deep in Southern Electric land rather than quite close to a couple of tube lines. It is this that makes parking somewhere like Osterley an inadequate solution IMHO.
A route planner or a SatNav would probably take you along the South Circular Road (A205) - quite a congested and torrid route at the best of times. I think I would consider coming right around the M25 to J7 and then turning onto the M23 towards central London. You would then have two choices - either drive to the ground, leaving the A23 at Thornton Heath Pond (going straight on onto the B266 where the A23 takes a left turn) - or park at or near Coulsdon South station and take the train from there to Norwood Junction (13-20 minute journey time; some journeys require a change of trains at East Croydon).
Perhaps people who live in south-east London will have better suggestions.
Best of luck.