Does the PS2 come with an RF modulator to connect it to the TV's aerial input? If so connect to the TV's aerial input instead of AV inputs, see if it works OK on RF.
NB. Apparently Toshiba had a compatibility issue with Nintendo Gamecube and this model or similar model involving sync problems with it's progressive scan output connected AV4. I don't know much about playstations or if there is any connection to this but the Nintendo problem required a small circuit change (added resistor) to the Toshiba's sync input.
Cobweb
October 2004